Angular-Resolved Polarized Surface Enhanced Raman Spectroscopy

Article pubs.acs.org/JPCC

Angular-Resolved Polarized Surface Enhanced Raman Spectroscopy Yusuke Nagai, Tatsuya Yamaguchi, and Kotaro Kajikawa* Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan S Supporting Information *

ABSTRACT: Surface immobilized gold nanospheres (SIGNs) on a metallic substrate are widely used for surface enhanced Raman scattering (SERS) spectroscopy. Since SIGNs significantly enhance the local electric fields of light, due to localized surface plasmon resonance, it is a highly promising SERS platform. To understand the mechanism of enhancement of Raman scattering in the presence of colloidal metals, it is necessary to know how the molecules are adsorbed on the SIGNs. We performed angular-resolved polarized SERS (AP-SERS) spectroscopy to probe the adsorption structure of the molecules on the SIGN. A theoretical analysis is given for the APSERS from the molecules on the SIGNs, based on the quasi-static approximation and the local field approximation. The molecules are adsorbed only in the upper hemisphere region of the SIGN in the high coverage SIGN substrate, whereas at low coverage, the molecules are adsorbed in both upper and lower regions. This is because the solution does not intrude into the space between the nanospheres, as a result of the surface tension of ethanol. This result explains the unstable and irreproducible SERS signal from the aggregated nanospheres. (SHG),18−20 photoluminescence, and sensitive detection of biological molecules.21,22 A number of SERS measurements have also been reported using SIGN platforms, with a SERS enhancement factor of ∼105.23 The advantage of the SIGN platform over isolated gold nanoparticles and their aggregates formed on a glass substrate is that the SIGN structure is well-defined. The gap distance can be controlled by varying the thickness of the supporting gap layer, and the number of gold nanospheres (including their images) in a single structure is exactly two, that is, a dimer. Hence, we can calculate theoretically the enhanced electric fields around the SIGN,15,24,25 and it is possible to predict and measure the linear and nonlinear optical responses from the SIGN.18,19,26 To determine the mechanism of SERS, it is necessary to know how the molecules are adsorbed on the SIGN. Recently, we have solved this problem, using polarized SHG. This solution is applicable only to SHG active molecules, however. We study below how the molecules are adsorbed on the SIGN, using angular-resolved polarized SERS (AP-SERS) spectroscopy. Although polarized SERS spectroscopy is powerful for detailed probing of adsorbates on a metallic surface, few studies have used it.27−31 This is because the structures of most SERS-active platforms are complicated, and it is difficult to analyze the SERS signal. The SIGN structure is simple and widely used for SERS measurements.32−35 Thus, it is worth developing the analysis for the AP-SERS signal from the

1. INTRODUCTION Surface enhanced Raman scattering (SERS) spectroscopy is a powerful optical tool for probing organic and biological molecules and pathogens.1−8 The greatly enhanced local electric fields generated at a rough surface or at colloidal metals are the main cause of the great enhancement of the Raman scattering signal. The large enhancement of the electric field is due to localized surface plasmons (LSP) in the nanometer-scale metallic structures. Consequently, SERS makes it possible to detect very small numbers of molecules even down to single molecular level.9,10 Many studies have aimed to create efficient SERS-active platforms. Of the various SERS-active platforms, gold nanoparticles and their aggregates are widely used, since intense Raman signals can be obtained, even with the simple fabrication process. In particular, silver or gold colloidal aggregates deposited on a glass substrate exhibit single molecule sensitivity, because of the enhanced electric field of light localized at the junction of the nanoparticles.9,11−13 The enhanced local electric field is much greater than that localized around isolated particles. Many single molecule SERS observations have been reported, using silver colloid aggregates. Another LSP platform involving colloidal metals is surface immobilized gold nanospheres on a metallic substrate (SIGN). Since the mirror image is produced in the metallic substrate, the SIGN structure is almost equivalent to a gold dimer.14,15 As a result, a greatly enhanced electric field is generated in the nanogap between the gold nanosphere and the gold surface. A LSP resonance band therefore appears, red-shifted from the resonance band of the isolated gold nanospheres.15−17 The SIGN platform is effective for second harmonic generation © 2012 American Chemical Society

Received: November 22, 2011 Revised: March 27, 2012 Published: March 29, 2012 9716

dx.doi.org/10.1021/jp211234p | J. Phys. Chem. C 2012, 116, 9716−9723

The Journal of Physical Chemistry C

Article

Figure 1. Optical setup used for the AP-SERS measurements.

Figure 2. (a) Geometry of SIGN used for calculation; (b) definition of the cap angle, θcap; and (c) local rectangular (u, v, w) and molecular (l, m, n) coordinates at point Q. The molecule is located at r = 1 (the nanosphere surface).

promote adhesion between the glass slide and the thin gold film. The substrate was immersed in the ethanol solution of AUT for 3 h so as to form an AUT self-assembled monolayer (SAM) on the gold thin film. It was then rinsed with 2propanol. After that, the substrate was immersed in an aqueous solution of the gold nanospheres, to form the SIGN substrate. The coverage of SIGNs, σ, was evaluated by scanning electron microscopy (SEM), which we performed with a JSM-6610LA scanning electron microscope (JEOL, Japan) in the Center for Advanced Materials Analysis, Technical Department of Tokyo Institute of Technology. The low coverage (σ = 5%) SIGN substrate was fabricated by immersion of the substrate for 2 h with no stirring, and the low coverage substrate with σ = 10% was fabricated by immersion of the substrate for 2 h with stirring. The high coverage substrate with σ = 35% was made by immersion for 24 h with stirring. The substrate was rinsed with Millipore water to remove any gold nanospheres binding weakly to the AUT SAMs on the substrate. For adsorption of R6G molecules onto the SIGNs, the substrate was immersed in the R6G ethanol solution for 24 h. It

platform. We found that the molecules are adsorbed only in the upper hemispherical regions at high coverage, whereas at low coverage, the molecules are adsorbed in both upper and lower regions. This is because the ethanol solution involving the SERS-active molecules for immersion of the substrate does not intrude into the space between the SIGNs.

2. EXPERIMENTAL SECTION We used gold nanoparticles of diameter 80 nm, purchased from Tanaka Kikinzoku Kogyo K. K., Japan. For SERS-active molecules, Rhodamine 6G (R6G) and 4-aminobenzenethiol (ABT) were purchased from Sigma Aldrich Co. and were used as received. They were dissolved in an ethanol solution, at concentrations of 5 μM for R6G and 1 mM for ABT. Aminoundecanethiol (AUT) was purchased from Dojindo Laboratry, Inc., Japan, and was used as received. It was dissolved in ethanol at a concentration of 0.1 mM. The SIGN platform was fabricated on a glass slide. A 2 nm thick chromium thin film and a 50 nm thick gold thin film were vacuum-evaporated. The chromium thin film was used to 9717



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Supporting Information. The expression was derived using the quasi-static approximation. The Raman scattering intensity I Q (θ, ϕ) from an infinitesimal element dϕ sin θ dθ at a point Q on the sphere surface r = 1, probed by a detector, is expressed as follows:

was used without rinsing. The ABT SAMs on the SIGNs were formed by immersion of the substrate in the ABT ethanol solution for 24 h. The substrate was then rinsed with 2propanol. The optical setup for AP-SERS spectroscopy is shown in Figure 1. The light source was a continuous-wave frequencydoubled Nd/YAG laser (λ = 532 nm, GLM-D2, Edmond Optics Inc., USA). The output power was less than 1 mW. A color filter was used to eliminate the leaked light from the laser. The incident light was focused with an objective lens (50×, 0.55 N.A.) after choosing the polarization with a film polarizer and a half-wave plate. The sample was installed on a rotation stage in order to vary the angle of incidence. The scattered Raman light was collected with the objective lens and focused on an endface of the optical fiber. A film analyzer was used to select the polarization of the scattered Raman light. A notch filter at 532 nm was installed to block the excitation light. The light was conveyed to a MS127 spectrometer (Oriel, USA), and the signal was taken with a DV-4010BV cooled CCD camera (Andor Technology, UK). The temperature of the CCD device was maintained at −50 °C, using a Peltier device; the typical accumulation time was 10 s for R6G-adsorbed on SIGNs and 2 min for the ABT SAM-adsorbed specimens.

IQ (θ , ϕ)dϕ sin θ dθ uvw

⃡ (r , θ , ϕ) + α⃡ (ωR ) · = C⟨| eout ⃗ ·(Txyz uvw ⃡ (r , θ , ϕ) ·X⃡ ) ·χ⃡ ·E ⃗loc(r , θ , ϕ)|r2= 1⟩dϕ Txyz sin θ dθ 2 = C⟨| eout ⃗ ·K⃡ ·χ⃡ ·E ⃗loc(r , θ , ϕ)|r = 1⟩dϕ sin θ dθ

(3)

where uvw

uvw

⃡ (r , θ , ϕ) + α⃡ (ωR ) ·Txyz ⃡ (r , θ , ϕ) ·X⃡ K⃡ = Txyz

(4)

Here, α⃡ (ωR) is the polarizability tensor of the SIGN at the Raman frequency ωR, χ⃡ is the Raman tensor of the adsorbates in the local coordinates (u, v, w) at point Q. T⃡ uvw xyz (r, θ, ϕ) is the transformation matrix from the local coordinates (u, v, w) at Q(r, θ, ϕ) to the sample coordinates (x, y, z), and C is a R constant coefficient. eo⃗ ut is a tensor product of L⃡ ωmac and unit R R ⃡ vector of the output polarization, êout, that is, eo⃗ ut = Lωmac êout. L⃡ ωmac is the macroscopic local field factor at the Raman frequency, ωR, which will be considered later. The tensor X⃡ is an operator that gives the electric field at the origin, produced by a dipole at the sphere surface. It is given in the Supporting Information. The matrix K⃡ consists of two components. The first term gives the radiation field from the dipole at point Q, and the second term does the radiation field produced by the dipole through the SIGN. The distance between the detector and the origin is much larger than the particle radius R, the radiation field can be regarded as a plane wave, and the two components can be simply added. Since the polarizability of the SIGN α⃡ (ωR) is calculated as a result of the multipole expansion until 15th order, it involves the contribution of the multipoles. For the calculation of SERS intensity, many previous works have employed the reciprocity theorem and have described the SERS intensity in a simple form.27,28,30 It has been also used for the calculation of SHG or two photon photoluminescence intensity from metallic nanostructures.36−38 However, the theory does not hold in our case because of the following two reasons: (a) the matrix X⃡ causes the matrix K⃡ noninterchangeable with eo⃗ ut, and (b) the reciprocity theorem is originally designed for dipole radiation.28 The limitation of the reciprocity theorem is also suggested by Chen et al. in eq 4 of ref 36 and is reported experimentally by Le Ru et al.40 The angular brackets in eq 2 denote an average over the molecular orientational distribution. The polarizability α⃡ (ωR) is given by calculating multipoles in a SIGN, at the Raman frequency, as reported previously,24,45,46 and is also given in the Supporting Information. It consists of two components: the first-order multipole coefficient for the electric field normal to the surface, A1, and that for the electric field along the surface, B1. Since the Raman scattering is incoherent, the total signal intensity, ISERS, is the sum of the intensity from each infinitesimal element

3. THEORETICAL ANALYSIS FOR AP-SERS We now describe how the AP-SERS signal was analyzed. The optical geometry of the SIGN platform is shown in Figure 2(a). It is the basis for the theoretical calculation of the SERS intensity from the SERS-active molecules adsorbed on the SIGN with polar angle θcap, as shown in Figure 2(b). The polar angle θcap is the angle to be evaluated by the following experiments and calculations. A gold nanosphere of radius R (medium 3) is located in an ambient medium of air (medium 1) on an ultrathin film of AUT (medium 4), with a gap distance d. The AUT SAM is deposited on a gold substrate (medium 2). The permittivity of the ith medium is denoted by εi. The center of the nanosphere is chosen as the origin of the Cartesian (x, y, z) and spherical polar (ρ, θ, ϕ) coordinates. From now on, we use a parameter r (r = ρ/R), instead of ρ, for convenience. When a field of excitation light, E⃗ inc, is incident to the sample, a macroscopic electric field, E⃗ mac, is generated. In general, E⃗ mac ≠ E⃗ inc, because of the electromagnetic interaction between the SIGNs.17,41−44 The relation between them will be considered below. Here, we start the situation that the macroscopic electric field E⃗ mac is applied to the SIGN. The application of the electric field of light E⃗ mac to the SIGN produces the local electric field E⃗ loc(r, θ, ϕ) at point Q(r, θ, ϕ) in the local rectangular coordinates (u, v, w). The local electric field is described as the product of the local field tensor L⃡ (r, θ, ϕ) and the macroscopic electric field E⃗ mac: ⃗ E ⃗loc(r , θ , ϕ) = L⃡ (r , θ , ϕ)Emac

(2)

(1)

The local rectangular coordinates (u, v, w) is defined as shown in Figure 2(c). The directions of the axes u, v, and w are defined as the directions of polar, azimuthal, and radial, respectively. The introduction of the local coordinates (u, v, w) is necessary, since the Raman tensor components depend on the position in the sample coordinates (x, y, z). The general expression for the local field tensor L⃡ (r, θ, ϕ) at point Q has been given in our previous papers, which treat that SHG fields from adsorbates covering the SIGN,45,46 and is also given in the

ISERS = C

∫0

θcap

sin θ dθ

∫0

2π

dϕIQ (θ , ϕ)

(5)

The constant C is canceled by taking a ratio of Raman signal intensity measured at two different polarization combinations, 9718



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ss ij that is, η = Ipp SERS/ISERS. Here, ISERS stands for the Raman intensity measured with i-polarized excitation and j-polarized detection. The definition of the polarization direction is shown in Figure 2(a). When the interparticle distance is large, that is, at low coverage, the electromagnetic interaction between the SIGNs is negligible. The electric field applied to the SIGN, E⃗ mac, can then be taken to be the same as the electric field of the incident light, E⃗ mac = E⃗ inc. The Raman intensity ratio η can then be calculated without considering the interparticle interactions. When the interparticle distance is small, the interaction should be taken into account, so that E⃗ mac ≠ E⃗ inc. We have reported that the interparticle interaction is negligible with coverage less than 8% for SIGNs within 10% accuracy.17 At coverage 8−80%, the interparticle interactions of electric dipoles must be considered. At higher surface coverage, above about 80%, it is necessary to evaluate the interparticle interaction over the multipoles. The analysis is given in the Supporting Information. The highest coverage of the SIGNs used in this study is 35%. To determine the interparticle interaction, we compute the contribution from the first- and second-nearest neighbor nanospheres using the square lattice model with a lattice constant a, as shown in Figure 3. The contribution from more

ω

L⃡mac0

⎛ ⎞ 1 0 0 ⎜ ⎟ 3 + ξα 1 /(2 a ) xx ⎜ ⎟ ⎜ ⎟ 1 ⎟ 0 0 =⎜ 1 + ξαyy/(2a3) ⎜ ⎟ ⎜ ⎟ 1 ⎜ ⎟ 0 0 ⎜ ⎟ 1 − ξαzz /(a3) ⎠ ⎝

(8)

where ξ is computed to be −5.42 and αii (i = x, y, or z) is a component of the polarizability tensor at ω0. The macroscopic R local field factor L⃡ ωmac at the Raman frequency, used for emission, can be also described similarly. To calculate the Raman intensity ratio, η, the Raman tensor χ is needed. For C−S band stretching at 1086 cm−1 in the ABT SAMs, we assume that the Raman tensor component normal to the surface χww is dominant in the local coordinates (u, v, w) at point Q, where the axis w is set to be the surface normal, since the molecules are regarded to be well ordered along the surface normal in the SAM. In contrast, we assume that the R6G molecules are assumed to be randomly oriented in this analysis, since R6G has no groups anchor to the gold surface in its chemical structure. We therefore consider here the Raman tensor components when the molecules are randomly oriented. Assume a molecular principal Raman polarizability tensor β⃡ along the principal axes (l, m, n), as shown in Figure 2(c), where the axis l is tilted with respect to the axis u with a polar angle ξ, and an azimuthal angle ζ is defined from the axis v. The rotation angle ψ is about the principal axis l. When the molecules are randomly oriented, the angular bracket in eq 2 is transformed to the integrals:30 IQ (θ , ϕ)dϕ sin θ dθ

∑ i

3 ri ⃗ ri ⃗ − | ri |⃗ 2 | ri |⃗ 5

⃗ α⃡ (ω0)Emac

⃗ = Emac

∫0

lmn R⃡ uvw

sin ξ dξ 2π

∫0

2π

dζ

2 dψ| eout ⃗ ·K⃡ ·χ⃡ ·E ⃗loc(r , θ , ϕ)|r = 1dϕ sin θ dθ

⎛ cos ζ − sin ζ 0 ⎞⎛ cos ξ 0 sin ξ ⎞⎛ cos ψ − sin ψ 0 ⎞ ⎜ ⎟⎜ ⎟⎜ ⎟ = ⎜ sin ζ cos ζ 0 ⎟⎜ 0 1 0 ⎟⎜ sin ψ cos ψ 0 ⎟ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎝ 0 0 1⎠ 0 1 ⎠⎝− sin ξ 0 cos ξ ⎠⎝ 0 (10)

When a single vibration along the axis l is dominant for the Raman process, the molecular Raman tensor β⃡ consists of a single component βll. Then, nonzero averaged χ tensor components are ⟨χ2ii⟩ = (1/5)β2ll and ⟨χiiχjj⟩ = ⟨χ2ij⟩ = (1/15)β2ll, where i, j = u, v, or w. Using the averaged χ tensor components, IssQ(θ, ϕ) and Ipp Q (θ, ϕ) are reduced to the following:

(6)

where ri⃗ is the position vector from the origin to the surrounding SIGN i and α⃡ (ω0) is the polarizability of the SIGN at the excitation light frequency ω0. The second term describes electric field at the origin produced by the surrounding eight dipoles of the SIGNs. The relation between the two fields is as follows: ω ⃗ L⃡mac0 E inc

×

π

The Raman tensor χ⃡ in the coordinates (u, v, w) is connected to the Raman tensor β⃡ in the molecular coordinates (l, m, n) as ⃡ ⃡ lmn −1 ⃡ lmn χ⃡ = R⃡ lmn uvw·β·(Ruvw) , using the rotation tensor Ruvw from molecular (l, m, n) to local (u, v, w) coordinates.47 The rotation tensor is as follows:

distant nanospheres other than those will be screened, since the size of the nanospheres are of the order of the lattice constant a. We use the local field approximation (LFA),17,41−45 according to which each SIGN is equivalent. The applied electric field is the sum of the incident light field and the contribution from the surrounding eight SIGNs: 8

∫0

(9)

Figure 3. Geometry of the square lattice used for calculation of the macroscopic local field tensor L⃡ mac.

⃗ = E inc ⃗ + Emac

=C

IQss (θ , ϕ) = 2Cβll2(f1 Eu2 + f2 Ev2 + f3 Ew2

(7)

+ 4(f4 EuEv + f5 EvEw + f6 EwEu))

0 L⃡ ωmac

where is the macroscopic local field tensor that relates E⃗ inc 0 to E⃗ mac. Under the LFA, L⃡ ωmac is given by the following:

(11)

and 9719



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(c), the interparticle interaction is neglected. In (b) and (d), the macroscopic local field tensors at a = 3R were taken into account. As shown in Figure 4, η is unity at the normal incidence (Θ = 0). There η increases from unity with increasing angle of incidence Θ when the cap angle θcap is small (θcap < 90°). The increase is remarkable for smaller θcap. This is because the normal component of the electric field of the p-polarized incident light increases with Θ and the molecules located at small polar angles contribute to the SERS signal. When the cap angle exceeds 90°, the s-polarized light contributes to the SERS for the molecules located at around θ ∼ 90°, and η decreases from unity with increasing Θ. In the profiles (b) and (d) (highcoverage platforms), the decrease in η at oblique incidence is more significant at larger θcap. In profiles (a) and (c) (lowcoverage platforms), however, the decrease in η at oblique incidence with Θ is greatest at θcap = 120°, and the decrease in η is less at larger θcap, more than 120°. We cannot therefore distinguish between the profiles at θcap = 80−120° and those at θcap = 120−150°, since the two profiles almost overlap.

IQpp(θ , ϕ) = Cβll2(Eu2(g1 + g2cos2 2Θ + g3sin 2 2Θ) + Ev2(g4 + g5cos2 2Θ + g6 sin 2 2Θ) + Ew2(g7 + g8cos2 2Θ + g9sin 2 2Θ) + 4EuEv(g10 + g11cos2 2Θ + g12 sin 2 2Θ) + 4EvEw(g13 + g14 cos2 2Θ + g15sin 2 2Θ) + 4EwEu(g16 + g17cos2 2Θ + g18sin 2 2Θ)) (12)

where Θ is the angle of incidence. In eqs 11 and 12, Ei′s (i = u, v, w) are the components of the local electric field Eloc in the local coordinates at point Q. f i′s and gi′s are composed of the components of the matrix K⃡ , which are given in the Supporting Information. We calculated the Raman intensity ratio, η, as a function of the angle of incidence Θ, at different cap angles θcap. η can be calculated without using C or βll, because they are canceled. We used the gap distance of d = 0.66 nm that is evaluated from the peak wavelength in the reflection absorption spectroscopy and from calculation.16 The gold nanosphere radius of 40 nm enters the calculation, and the permittivity of gold reported in the literature.48 Two cases are considered that the SIGNs are isolated (no interparticle interaction is taken into account) and that the nanospheres are separated with a gap distance of R (a = 3R). In the latter case, the corresponding coverage of the nanosphere is approximately 35%, at which value the macroscopic local field tensor L⃡ mac must be considered. The interparticle interaction is taken into account as a result of dipole radiation, since it is dominant if a > 2R, as shown in the Supporting Information. Results are shown in Figure 4 for the following: (a) R6G-adsorbed on isolated SIGNs, (b) R6Gadsorbed on SIGNs with interparticle interactions, (c) the ABT SAM-adsorbed on isolated SIGNs, and (d) the ABT SAMadsorbed on SIGNs with interparticle interactions. In (a) and

4. RESULTS AND DISCUSSION We examined four samples. Sample A is the R6G-adsorbed SIGNs at low coverage (σ = 10%). Sample B is that at high coverage (σ = 35%). Sample C is the ABT SAM-adsorbed SIGNs at low coverage (σ = 5%), and sample D is that at high coverage (σ = 35%). The coverage of SIGNs is evaluated by the SEM images, shown in Figure 5. The low coverage SIGN substrate at 10% and 5% are shown in Figure 5(a) and (b), respectively, and the high coverage substrate at 35% is shown in Figure 5(c). The difference in the coverage for the two low coverage samples (σ = 5% and 10%) is the result of stirring. Both substrates exhibit similar optical properties, since the SIGNs are isolated on either substrate. The SEM image shows that the SIGNs are free from aggregation, even at high coverage. This calculation is supported by the fact that the absorption peak attributed to the aggregated particles appearing at 600−900 nm is not observed in the reflection absorption spectrum taken at normal incidence. Figure 6 shows the SERS spectra of samples B for R6G and D for an ABT SAM. The main peaks are R6G at 622 cm−1 (C− C−C ring in-plane bending) and ABT at 1086 cm−1 (C−S stretching). The identity of each peak is summarized in Table 1, which is consistent with the previous reports.49,50 Figure 7 shows the measured intensity ratio η of samples A− D, as a function of angle of incidence, Θ. The most probable η profiles simulated are also indicated with solid lines at different θcap values. In the simulation, the interparticle interactions are taken into account, except for the sample C (σ = 5%). In addition, the contribution from R6G molecules adsorbed on the surface is ignored, since they give little contribution (the difference is ∼10°) for the determination of the θcap, as described in the Supporting Information. In sample A, the measured η profile matches two profiles at θcap = 65−75° and θcap = 160−170°, on the assumption that the molecules are randomly oriented. The former is too small to be considered as a cap angle of the sample at low coverage. Most of the SIGN surface must be exposed to the R6G solution and will be covered with the R6G molecules. Hence, we exclude the cap angle θcap = 65−75°, so that we determined θcap to be approximately 165°. This means that the molecules do not fully cover the SIGNs, even at low coverage, because there is a narrow space below the nanosphere where the molecules are

Figure 4. Calculated η profiles at various θcap values for: (a) R6G adsorbed on isolated SIGNs, (b) R6G adsorbed on SIGNs with interparticle interactions, (c) ABT SAM-adsorbed on isolated SIGNs, and (d) ABT SAMs adsorbed on SIGNs with interparticle interactions. 9720



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Figure 5. SEM images used for (a) sample A (σ = 10%), (b) sample C (σ = 5%), and (c) samples B and D (σ = 35%).

Figure 6. SERS spectra for (a) sample B and (b) sample D.

Table 1. Raman Peaks Observed in the Spectra of R6G and ABTa peak wavelength (cm−1) molecule

in literature

observed

assignment

R6G

614 744 1363 1509 1650 1089 1595

622 780 1369 1514 1652 1086 1590

C−C−C ring ip bend C−H op bend arom C−C str arom C−C str arom C−C str C−S str C−C str

ABT a

Figure 7. Observed η profiles for (a) sample A, (b) sample B, (c) sample C, and (d) sample D. The solid lines are most probable η profiles simulated at different θcap angles.

Finally, we consider the reason for the small cap angle in samples B and D, using the theory of Extrand,51 which was developed to explain the repellency of a lotus leaf. Suppose that the SIGNs are located in a square lattice with a lattice constant a, as shown in Figure 3. The cross section view is shown in Figure 8, in which the liquid surface tension γ and the

Bend: bending; str: stretching; ip: in-plane; op: out-of-plane.

difficult to intrude. This result is consistent with our exploration based on SHG and Monte Carlo simulation.26 For sample B, a unique lower θcap = 50−60° is matched, in which part of the upper hemisphere is covered with R6G molecules and molecules are absent in the lower hemisphere. In contrast to sample A, this result is possible, since the coverage is high. The reason for the low cap angle in sample B is discussed below. The measured η profile of sample C shown in Figure 7(c) also matches two profiles at θcap = 60−75° and θcap = 160−175°, supposing that the molecules are well ordered on the SIGNs. Because of the same reason in sample A, the lower range is excluded, so that sample C has θcap = 160−175°, which is consistent with our exploration based on SHG.26 The η profile of sample D matches a unique profile at θcap = 55−60°. Part of the upper hemisphere is covered with ABT SAMs; these are absent from the lower hemisphere. In samples at high coverage (samples B and D), θcap is found to be less than 90°. The molecules are adsorbed only in the upper hemisphere region and are barely adsorbed on the junction when the spheres are close or aggregated. This explains why the intense SERS signal from the gap region between the nanospheres is unstable and irreproducible.

Figure 8. Geometry for calculation of the repellency of the solution.

hydrostatic pressure p are balanced at an intrusion angle of θa. The contact angle of the liquid with the nanosphere surface is θc. The hydrostatic pressure p is the product of three parameters: the density ρ, the gravitational acceleration g, and the depth of the substrate h on immersion of the substrate in the liquid. When the vertical component of the capillary force 9721



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and the hydrostatic pressure are balanced, the relation is given by the following: sin θa sin(θa + θc) =

p(4a 2 − R2π sin θa) 2πRγ

(13)

For h ∼ 100 mm and γ = 25 mN/m for ethanol, the left-hand side is close to zero; the force due to the liquid surface tension is much larger than that from the hydrostatic pressure. The intrusion angle θa is then determined solely by the contact angle θc, and the solution of eq 13 gives θa = π − θc. The contact angle is influenced by the surface structure of the nanosphere. The contact angle θc of a smooth gold surface is ∼70°. However, roughness at the surface causes an increase of the contact angle by π/2 at the maximum.52,53 The intrusion angle θa therefore varies from 20° to 110°. The gold nanosphere surface will be slightly rough; it is likely that the intrusion angle θa is around 70°, a value consistent with the present experimental results.

5. CONCLUSION We have studied how molecules are adsorbed on SIGNs, using AP-SERS spectroscopy. An analysis of the AP-SERS signal from the SIGN platform is given, and the experimental results are analyzed. The molecules are adsorbed only on the upper hemispherical regions of the nanosphere at high coverage, whereas at low coverage the molecules are adsorbed in both upper and lower regions. This is because the SIGNs exhibit repellency to the ethanol solution, which does not intrude into the space between the nanospheres. The repellency comes from the surface tension of the ethanol. This result indicates that the repellency will be a reason for the unstable and irreproducible SERS signal observed from the aggregated nanospheres.

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ASSOCIATED CONTENT

S Supporting Information *

Details on the local field tensor and polarizability, electric field calculation considering the contributions of dipoles and multipoles, the comparison of eq 2 to the reciprocity theorem, the Raman intensity, and the contribution of R6G molecules adsorbed on the substrate surface, and further references. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +81-45-924-5596; fax: +81-45-924-5596; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Center for Advanced Materials Analysis, Technical Department of Tokyo Institute of Technology, for SEM analysis. This work was partly supported by Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

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REFERENCES

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Angular-Resolved Polarized Surface Enhanced Raman Spectroscopy

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