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Surface Morphology of a Gold Core Controls the Formation of Hollow or Bridged Nanogaps in Plasmonic Nanomatryoshkas and their SERS Responses Boris N. Khlebtsov, and Nikolai G. Khlebtsov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03606 • Publication Date (Web): 16 Jun 2016 Downloaded from http://pubs.acs.org on June 18, 2016

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Surface Morphology of a Gold Core Controls the Formation of Hollow or Bridged Nanogaps in Plasmonic Nanomatryoshkas and their SERS Responses Boris N. Khlebtsov a and Nikolai G. Khlebtsova,b,* a

Institute of Biochemistry and Physiology of Plants and Microorganisms, Russian Academy of Sciences, 13 Prospekt Entuziastov, Saratov 410049, Russia b

Saratov State University, 83 Ulitsa Astrakhanskaya, Saratov 410026, Russia

*Corresponding author: [email protected]; tel: +7(8452) 970403

Abstract

Surface-enhanced Raman scattering (SERS) probes with a nanometer-sized interior gap between Au core and shell, also called nanomatryoshkas (NMs), have attracted great interest in SERS-based bioimaging and biosensing. Recently, seed-mediated growth has been shown to be effective for NM synthesis. We found that the structure of nanogaps inside Au NMs depends strongly on the core surface morphology. Specifically, when the initially citrate-stabilized 15- and 35-nm smooth Au cores were further functionalized with 1,4 benzenedithiol (BDT) in the presence of cetyltrimethylammonium chloride (CTAC), the Au shell growth led to the formation of a sub-nanometer hollow interior gap

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containing BDT molecules. In contrast, the use of 23- and 35-nm faceted polygonal CTAC-stabilized Au cores for Au shell growth resulted in NMs with small bridged gaps. The formation of incomplete outer shells with one or two nanometer-sized hollow gaps was also observed for 23-nm polygonal cores, but not for 35-nm ones. The experimental SERS response from BDT molecules in bridged-gap NMs was an order of magnitude higher than that for hollow-gap NMs. This finding is in agreement with the finite-difference time-domain (FDTD) simulations predicting stronger electromagnetic fields inside nanobridged gaps, as compared to hollow-gap NMs. The major SERS peaks from BDT inside NMs of both types (two sizes, four samples) was an order of magnitude higher than the near-field SERS peaks recorded for the corresponding 15CIT, 23CTAC, 35CIT, and 35CTAC cores alone after surface functionalization with BDT molecules. This observation is explained by a simple dipole approximation (DA) theory, which was developed to estimate the structure- and wavelength-dependent electromagnetic SERS enhancement in the hollow-gap NMs with good accuracy, as confirmed by comparison with exact multilayered Mie (ML Mie) calculations. With a double increase in the core size, the NM SERS response also increased and the ratio between the major peak intensities of the larger and smaller NMs was about 2. Finally, the calculated SERS spectra of the hollow-gap NMs agree with the data reported for 532-, 633-, and 785-nm laser excitations. The physical insights acquired from this study open the way for rational design and efficient optimization of new SERS platforms based on electromagnetic field enhancement in sub-nanometer gaps within plasmonic nanostructures.

1. INTRODUCTION Recently, several research groups have reported on highly efficient multilayered SERS tags in which Raman molecules are trapped in a nanometer-sized interior gap between the metallic core and the shell.1-6 Such multilayered structures, also called nanomatryoshkas (NMs)7-9 or BRIGTHs2 (bilayered Raman-intense gold nanostructures with hidden tags) have great potential for biomedical applications4,5,10 owing to several advantages: (1) Raman molecules are protected from desorption and


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environmental conditions; (2) they are subjected to a uniform and strongly enhanced electromagnetic field in the gap; (3) NMs produce a stable SERS response even if aggregated; (4) the highly uniform spectral pattern ensures a linear correlation between probe concentration and SERS intensity; and (5) nanogap SERS probes can be multiplexed by incorporating different Raman molecules into twolayered4,5,11 or multilayered NMs9. The core–shell separation can be obtained by using dielectric or molecular spacers, thereby controlling the near-field enhancement between the core and the shell. This phenomenon has been explained by classical1,12 and quantum-corrected6,13,14 electromagnetic theory, which predicts electric field enhancements in the built-in nanogaps and its correlation with gap thickness and structure.12 From a practical point of view, this enhancement leads to a strong and uniform SERS response from such NMs with a fundamental enhancement factor (EF) of about 108. What is more, such high EF values can be distributed within a narrow range of 0.1 to 5 billions1 and they are higher than those reported for various SERS tags with surface-adsorbed Raman molecules. As a result, it has become possible to observe single-particle SERS responses with common Raman microscopes, thus opening the practical way for high-resolution cell imaging.5,10,11 Synthesis of gold NMs consists of three main steps: synthesis of a gold core, modification with Raman reporters and spacers, and growth of an outer gold shell. Thiolated Raman-active molecules such as 1,4-benzenedithiol (BDT) can form a gap inside a core–shell particle2,6 and serve both as the Raman active molecule and as the spacer. In this case, the gap size from high-resolution transmission electron microscopy (HRTEM) images2,6 is ~ 0.7 − 1 nm, in reasonable agreement with the thickness of a BDT monolayer. The concentration and chemical structure of ligands, as well as the size and shape of seeds, play an important role in the design of NMs and can greatly affect the interior structure of the ligand-mediated gaps. Specifically, the formation of hollow vs bridged gaps is of great interest, because the SERS response produced by bridged-gap nanostructures may be stronger than that from hollow structures. However, only few attempts have been made to deal with these important issues. For example, when a ACS Paragon Plus Environment


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subthreshold concentration of BDT (0.5 µM) was used to modify the surface of spherical Au nanoparticles, no interstitial gap was seen between the core and the shell, with a 75-nm uniform rhombic dodecahedron being observed instead.2 Lin et al.6 reported that the replacement of 1,4-benzenedithiol with 4-methylbenzenethiol leads to the formation of bridged gaps instead of hollow ones. Hwang et al.15 used DNA-functionalized Au nanorods as seeds to fabricate Au-nanobridged nanogap cucumbers with a bumpy surface. At 785-nm excitation, the SERS signals generated by those particles were up to 130fold higher than those from Au spheres with bridged nanogaps. The use of BDT-coated Au nanostar cores16 as seeds for outer shell growth in a BDT–CTAC (hexadecyltrimethylammonium chloride) ligand mixture results in various unusual nanostructures, with the semishell configuration being most SERS effective. Here, we demonstrate that the formation of hollow or bridged nanogaps in gold NMs and their SERS response are controlled by the seed surface morphology. Specifically, the use of citrate-stabilized smooth Au nanoparticles further functionalized with BDT leads to the formation of a sub-nanometer hollow interior gap containing BDT molecules. In contrast, for faceted polygonal CTAC-stabilized Au cores of the same size, the Au shell growth results in NMs with small bridged gaps, thus leading to an order of magnitude higher SERS response from BDT molecules in bridged-gap NMs as compared to their hollow-gap counterparts. To give some insight into the SERS properties of the NMs, we propose a simple dipole approximation theory and compare it with multilayered Mie and FDTD simulations.

2. EXPERIMENTAL AND THEORETICAL METHODS 2.1 Materials. All chemicals were obtained from commercial suppliers and were used without further purification. Cetyltrimethylammonium bromide (CTAB, > 98.0%), cetyltrimethylammonium chloride (CTAC, 25% solution in water; > 98.0%), L-ascorbic acid (AA, >99.9%), sodium citrate (tribasic) (NaCit, 99.99%), 1,4-benzenedithiol (BDT, 99%), and sodium borohydride (NaBH4, 99%) were all purchased from Sigma–Aldrich. Hydrogen tetrachloroaurate trihydrate (HAuCl4·3H2O) was from Alfa Aesar. Ultrapure water obtained from a Milli-Q Integral 5 system was used in all experiments ACS Paragon Plus Environment

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2.2 Synthesis of cores. For preparation of 15- and 35-nm polycrystalline citrate-capped Au cores17, 3.1 and 1.4 mL of 1% sodium citrate, respectively, were added to 100 mL of boiling 0.01% chloroauric acid on a magnetic stirrer in a 300-mL Erlenmeyer flask. Within 15 min, the color of the solution changed from colorless to orange–red (15-nm seeds) or to pink–red (35-nm seeds). Finally, 14.3 mL of a 0.8 M (25%) CTAC solution was added to each seed solution, which resulted in the formation of nanoparticles in 100 mM CTAC. The final concentration of Au was estimated to be about 54 µg/mL (Supporting Information, Table S1). For preparation of single-crystal18 CTAC-capped Au polygonal cores, a seed-mediated protocoll9 was used. In brief, a seed solution was first prepared by vigorous mixing of 10 mL of aqueous CTAC (0.2 M), 4.75 mL of water, and 250 µL of HAuCl4 (10 mM) with 600 µL of a NaBH4 solution (0.01 M).

The seed solution was allowed to age for two hours and then was diluted tenfold. Next, 50 mL of CTAC solution (0.1 M) was mixed with 1.5 mL of HAuCl4 (10 mM) and 300 µL of ascorbic acid (0.1 M). Finally, 600 or 100 µL of the diluted seed solution was added under sonication and the mixture was kept undisturbed for 30 min to obtain polygonal nanoparticles with average sizes of 23.2 and 34.6 nm, respectively. The statistical data on the average particle sizes, the particle number concentrations N (part/mL), and the specific surface of all particles per mL S (cm2/mL) are summarized in Table S1 (Supporting Information).

2.3 Synthesis of NMs. The protocol for NM synthesis was the same for both quasispherical and polygonal cores of different sizes. The obtained Au cores (10 mL) were mixed with 300 µL of BDT ethanol solution (2 mM) under vigorous sonication for 20 min. These modified cores were then washed three times by centrifugation at 10000 rpm for 10 min to remove excess reagent, after which they were dispersed in 5 mL of aqueous CTAC (0.1 M). The Au NMs were prepared by adding, under stirring, 150



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µL of Raman-reporter-modified core solution to the growth solution of 2 mL of CTAC (0.1 M), 60 µL of ascorbic acid (0.04 M), and 50 µL of HAuCl4 (10 mM). For brevity, the NMs synthesized with 15- or 35-nm citrate seeds are designated 15CIT-NMs and 35CIT-NMs, respectively. Similarly, 23CTAC-NMs and 35CTAC-NMs stand for the NMs fabricated with 23- and 35-nm polygonal crystalline seeds.

2.4 Measurements. Extinction spectra were measured with a Specord 250 spectrophotometer (Analytik, Jena, Germany). Transmission electron microscopy (TEM) images were recorded on a Libra120 transmission electron microscope (Carl Zeiss, Jena, Germany) at the Simbioz Center for the Collective Use of Research Equipment in the Field of Physical–Chemical Biology and Nanobiotechnology, IBPPM RAS, Saratov. For TEM measurements, the nanoparticles were centrifuged twice and redispersed in water, after which 10 µL of washed nanoparticles was deposited onto a microscopic grid. HRTEM images and electron diffraction patterns were recorded with a Tecnai G2 200 kV electron microscope (FEI, USA). SERS spectra of the cores and colloidal solutions of NMs were acquired with a Peak Seeker Pro 785 Raman spectrometer (Ocean Optics) in 1-cm quartz cuvettes under 785-nm irradiation (10 mW). The influence of nanoparticle absorption (the inner-filter effect) was excluded by focusing the laser beam on the near cuvette wall. The acquisition interval was 30 s, and all SERS spectra were averaged over 10 independent runs.

2.5 Simulations. For electromagnetic simulations of hollow-gap NMs, we used a multilayered Mie solution (ML Mie),19,20 with some modifications, to calculate the surface-averaged internal field in the NM gap and the surface-averaged near field around the NMs. In addition, a simple dipole approximation (DA) was developed and compared with exact ML Mie simulations. In the case of bridged-gap NMs, we used a finite-difference time-domain commercial solver (FDTD Solutions 8.0,


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Lumerical Solutions, Inc.). Typically, the simulation mesh size was 1 nm and the input wavelengths ranged from 300 to 1100 nm.

3. RESULTS 3.1 NM synthesis and characterization Figure 1 shows TEM images of 15- and 35-nm citrate Au nanoparticles used as cores for the further fabrication of 15CIT-NMs and 35CIT-NMs, respectively. Table S1 (Supporting Information) summarizes the statistical data on the average size, the mass-volume concentration, the particle number concentration, and the specific surface of as-prepared citrate and CTAC core particles. Figure S1 (Supporting Information) presents a typical size-distribution histogram with a typical relative standard deviation (RSD) of about 10%.21

Figure 1. TEM images of 15-nm citrate (a), 23-nm crystalline (b), 35-nm citrate (d), 35-nm crystalline seeds (e), and their extinction spectra (curves 1 and 2 for citrate and crystalline seeds, respectively). The dotted curves illustrate a small red shift of spectra after functionalization with BDT. The insets show enlarged images.



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According to our previous observations,Error! Bookmark not defined.,22 the shape of larger citrate particles becomes slightly elongated. By contrast, the polygonal shape of the CTAC seeds was similar for both 23-nm and 35-nm particles. The extinction spectra of both particle types were quite similar, although some broadening could be seen for the 35-nm citrate seeds. Functionalization with BDT resulted in a small red shift of the plasmonic peak, as expected. Experimental observations showed6 that for the synthesis of nanobridged NMs, only freshly prepared polygonal cores should be used. Otherwise, as early as after two-week aging, the shape of the core particles becomes smoother, prohibiting their use in further work. These observations are illustrated in Fig. 2, in which TEM images of as-prepared CTAC cores are shown in panel (a) for comparison with the same particles 14 days after (b). Note that such subtle modifications of the particle shape only resulted in minor changes in the absorption spectra (Fig. 2c).

Figure 2 TEM images of as-prepared 35CTAC-NMs (a), the same particles after 14-day aging (b), and their extinction spectra (1) and (2), respectively. Figure 3 represents typical overview and enlarged TEM images of the NMs fabricated with the use of citrate and CTAC polygonal cores, together with the corresponding extinction spectra. In the case of the citrate cores, functionalization with BDT followed by additional Au shell growth yielded hollow gaps that separated the Au core from the shell. In panels (a) and (d), those gaps are marked by red arrows. As the gap thickness varied significantly, we used HRTEM images for statistical estimations (see below).


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Figure 3. TEM images of 15CIT-NMs (a), 23CTAC-NMs (b), 35CIT-NMs (d), and 35CTAC-NMs, as well as their extinction spectra (c, f), represented by curves 1 (citrate seeds) and 2 (polygonal seeds), respectively. The red and light green arrows show hollow and bridged gaps, respectively. Note the presence of NMs with incomplete hollow outer shells in panels (b) for 23-nm polygonal cores, but not for the other NM types. The insets show enlarged images. The left-middle inset in panel (a) shows 0.7−1-nm typical hollow gaps formed with 15-nm citrate seeds. In contrast to the 15CIT-NMs and 35CIT-NMs, the inner structure of the bridged-gap NMs was poorly resolved both with common TEM and with HRTEM. There was a difference in principle between the TEM-revealed structures of the 15CIT-NMs (Fig. 3a) and those of the 23CTAC-NMs (Fig. 3b). In the former case, we always observed complete outer gold shells, whereas for the 23CTAC-NMs, we observed a notable percentage of particles with incomplete, “mushroomlike” shapes. Such structures are marked by magenta arrows in Fig. 3b. Similar nanomushrooms have been observed previously for bimetallic Au-Ag nanoparticles with DNA-mediated nanogaps.23 The light green arrows indicate the bridged gaps within the CTAC-core-based NMs. The plasmonic peak is slightly shifted for the 15CITNM and 35CIT-NM pairs, but it is almost identical for the 23CTAC-NM and 35CTAC-NM pairs.



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To confirm the initial TEM observations and check the sample-to-sample reproducibility, we fabricated NMs by an independent run and then used HRTEM, as depicted in Figs. 4 and 5.

Figure 4. HRTEM images of 15CIT-NMs at increased magnifications (a, b, c). The red arrows show hollow gaps. The inset in the bottom of panel (d) shows 0.237-nm lattice fringes corresponding to the {111} interplane distance of Au. The left-upper inset shows the electron-diffraction pattern recorded from a group of particles (for details, see Figure S3 in the Supporting Information file). The high-magnification images in Fig. 4 clearly show hollow gaps of variable thickness. According to the statistical histogram (Fig. S4, Supporting Information), the gap thickness varied between 0.6 and 1.4 nm, with an average value of 0.86 ± 0.21 nm. Note that Lin et al.6 reported a gap-size histogram with three peaks centered at 0.72, 1.24, and 1.76 nm, corresponding to some hypothetical configurations of BDT within the gap. The magnified inset in Fig. 4d shows 0.237-nm lattice fringes corresponding to the {111} interplane distance of Au. Figure S3 and related analysis in Supporting Information by Eq. (S3) ACS Paragon Plus Environment

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give an interplane {1,1,1} distance of 0.237 nm, in good agreement with the value of 0.236 nm, calculated by Eq. (S6) (Supporting Information) by using the known lattice constant of Au and Miller indices {1,1,1}. The left-corner inset in Fig. 4d also demonstrates an electron diffraction pattern from a random particle group. By adjusting the contrast and brightness of the diffraction picture, we were able to identify several diffraction rings with high Miller indices (Fig. S4). The corresponding analysis is presented in Supporting Information and is summarized in Table S2.

Figure 5. HRTEM images of 23CTAC-NMs at increased magnifications (a, b, c). The red arrows show bridged gaps. The inset in the bottom of panel (d) shows 0.237-nm lattice fringes corresponding to the {111} interplane distance of Au. Figure 5 depicts typical HRTEM images for the 23CTAC-NMs with bridged gaps. The gap thickness is close to that for the hollow-gap NMs, but the size and number of gold bridges vary significantly



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among the different particles. The crystalline structure of the outer shell demonstrates 0.237-nm lattice fringes corresponding to the {111} interplane spacing of Au. Note that for the large, 35CTAC-NMs, we were able to reveal the bridged-gap inner structure only after the original HRTEM images had been adjusted to a higher overall brightness and to a higher brightness of the midtone values. To summarize this section, our TEM and HRTEM images, together with the electron diffraction patterns, confirm the formation of crystalline shells separated from the citrate cores by ~1-nm hollow gaps and separated from the polygonal CTAC-based cores by bridged gaps. In addition, the functionalization of the 23-nm CTAC cores with BDT followed by secondary Au shell growth gave rise to nanomushrooms with incomplete Au shells.

3.2. SERS measurements To elucidate the dependence of SERS responses on the NM structure and size, we compared the SERS spectra of BDT for the 15CIT- and 35CIT-NMs (hollow gaps, two sizes) with the SERS spectra of the 23CTAC- and 35CTAC-NMs (bridged gaps, two sizes close to those for the hollow-gap NMs) at a constant excitation wavelength of 785 nm. Figure 6 shows four experimental spectra (red curves 1) that give strong evidence that the SERS efficiency of the bridged-gap NMs is higher. Indeed, the major SERS peaks of the 23CTAC- and 35CTAC-NMs at 1064 cm-1 is an order of magnitude higher than those for their 15CIT- and 35CIT-NM counterparts. The second important point is a direct comparison of SERS responses from the BDT molecules located in the gap and on the surface of a core particle used for the synthesis of the corresponding NMs. In fact, the red and blue spectra in Fig. 6 show a direct comparison of the electromagnetic SERS efficiencies of the internal fields in the gaps and of the external fields around the plasmonic cores. By comparing the red and blue spectra in Figs. 6a-d, we arrive at the following important conclusion: the SERS inside the plasmonic NMs is an order of magnitude more efficient than that in similar near-field plasmonic platforms.


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Figure 6. SERS spectra of BDT recorded with the 15CIT-NMs (a), 23CTAC-NMs (b), 35CIT-NMs (c), and 35CTAC-NMs (d). Note the an order of magnitude difference between the ordinate scales in panels (a), (c) and (b), (d), respectively. For clarity, red spectra 1 in panels (a), (b), and (c) were shifted up by 400, 800, and 1000 Kcounts, respectively. In addition, blue spectrum 2 in panel (b) was multiplied by 10 and was shifted down by 800, while the blue spectrum in panel (d) was multiplied by 4. An accurate evaluation of size-dependent SERS enhancement is a challenging issue. According to preparation protocols, the total BDT concentration should be roughly the same in all samples. However, the number of SERS-active Raman molecules could not be estimated precisely for a particular sample. In our experiments, the larger NMs demonstrated a higher SERS amplification. For example, the ratio between the major peaks for the red spectra in Figs. 6c,a and Figs. 6d,b is about 2. However, the



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electromagnetic simulations (data not shown) gave a rather complex dependence of the electromagnetic SERS enhancement on the NM size and structure. Thus, the origin of possible physical mechanisms behind the above size-dependent ratio of 2 is still an open question. We cannot rule out that different numbers of Raman-active molecules could be present in NMs of different sizes. In Figure 7, the SERS signal of CTAC-NM is much stronger than the citrate-NM with similar size of core. This observations correlate with our FDTD simulations (see below, Figure 13). Those simulations were performed for three types of NMS: NMs with hollow gaps, NMs with bridged hollow gaps, and NMs with polygonal bridges gaps (Figure S5, Supporting Information). According to FDTD simulations, the maximal field amplification was observed for the second case. Of course, one should have in mind the nonuniform gap structure in the case of polygonal seeds and strong dependence of the gap field on the gap parameters. In general, the presence of nanobridged gaps is believed to be the main reason for more intense SERS response. The precise mechanism behind different morphology of citrate and polygonal NMs and their different SERS response (see below) is still not clear. The difference in stabilizing agents cannot be considered as a main reason for different gap structures, as the same CTAC quantity was added to both particle types. To distinguish the role of stabilizing agent and the particle morphology, we prepared polygonal CTACstabilized cores of 22 nm and 35 nm in diameter. Both seeds were aged for two weeks to achieve surface smooth morphology. Figure 7 illustrates the formation of hollow gaps in close analogy with formation of hollow gaps for citrate seeds. What is more, the SERS intensity was reduced drastically, almost to the level of SERS intensity from NMs obtained with 22-nm and 35-nm citrate seeds. These experiments give same evidence for possible leading role of the surface morphology rather than stabilizing agent.


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Figure 7. HRTEM images of 22CTAC-NMs (a) and 35CTAC-NMs (b) obtained after 24-day aging of as prepared polygonal seed. Clearly, the surface morphology has been transformed from polygonal to smooth one thus leading to formation of hollow gaps (indicated by red arrows). Panels (c) and (d) show the corresponding SERS spectra. Note that SERS signals from such NMs were decreased dramatically to the levels typical for 22CIT-NMs and 35CIT-NMs (see above, Fig. 6). In our previous studies, we investigated the SERS efficiencies for gold nanostar suspensions24 and for Au(core)@Ag(shell) nanorod assemblies.25 Here, we compared the SERS efficiencies for four types of colloids: (1) Ag nanocubes–BDT; (2) Au@Ag nanorods–BDT; (3) Au nanostars–BDT; and (4) 35CTAC-NMs. For the first three colloids, the BDT molecules were located on the particle surface, whereas for the last colloid, they were present in the internal gap. For all colloids, normalization was made to equal mass-volume core-metal concentrations, thus ensuring that the values of the specific colloid surface and the BDT concentrations were close.



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Figure 8. SERS spectra of the 35CTAC-NMs (1) in comparison with the SERS spectra of BDT adsorbed on gold nanostars (2), gold(core)/silver(shell) nanorods (3), and silver cubes (4). Panels (b), (c), (d), and (e) show TEM images of the 35CTAC-NMs, gold nanostars, gold (core)/silver (shell) nanorods, and silver cubes, respectively. Figure 8 shows illustrative TEM images of particles and a comparative set of SERS spectra. The main result of these experiments is as follows: the SERS enhancement of the 35CTAC-NMs is an order of magnitude higher than that for the other three types of surface-functionalized nanoparticles, whose efficiencies increase in the following order: Ag cubes, Au@Ag nanorods, and Au nanostars.

4. THEORETICAL SIMULATIONS 4.1. Field enhancement in the NM gap: the dipole approximation and comparison with ML Mie solution In this section, we analyze the enhancement of the internal gap field by using a simple electrostatic model. Although the external electrostatic problem for the polarizability of a multilayered sphere has ACS Paragon Plus Environment

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been solved many years ago, 26 no evaluations have been published of the electrostatic SERS enhancement in a plasmonic NM gap or of the accuracy of such an approximation. Here, we discuss these points very briefly; a more detailed analysis will be presented elsewhere. For simplicity, we consider a three-layered particle, although the methodology is applicable to an arbitrary multilayered particle. The particle structure is shown in Figure 8. For symmetry, the dielectric permittivity of the external medium ε m is designated as ε 4 ≡ ε m .

y a3,ε3

ε 4=εm

a2,ε2 E0 a1,ε1

x

Figure 9. Model for a three-layered particle with radii ai and dielectric permittivities ε i , i = 1, 2,3 . For symmetry, the dielectric permittivity of the external medium ε m is designated as ε 4 ≡ ε m . The electrostatic potential of an external homogeneous filed E0 is given by the following equation:

ϕ 0 = −E 0r ,

(1)

where E0 = 1 for simplicity. In the dipole approximation, the potential distributions in the four regions ( 1 − 4 ) can be written as follows:27

ϕi = − Ai E0r + Bi

ai3−1 E0r, i = 1 − 4, r3

(2)

where A4 = 1 . Further, as the internal field E1 should be homogeneous, we have to set B1 = 0 and

ϕ1 = − A1E0r . For the external potential ϕ4 , we have A4 = 1 . The boundary conditions are as follows:



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ϕi = ϕi +1 , r = ai , i = 1 − 3 ,

εi

∂ϕi ∂ϕ = ε i +1 i +1 , r = ai ∂r ∂r

(3)

i = 1 − 3.

(4)

After applying these boundary conditions to equation (2) and after some algebra, we arrive at the following equations: Ai = qi Bi − pi Bi +1 , i = 1 − 3 .

(5)

Ai +1 = d i Bi − bi Bi +1 , i = 1 − 3 ,

(6)

f (1 + 2γ i ) 3 , qi = i , 1− γ i 1− γ i

(7)

εi a3 , f i = i −31 , ε i +1 ai

(8)

2 +γi 3fγ , di = i i , 1− γ i 1− γ i

(9)

or, in other form,

where

pi =

γi =

bi =

From the above equations, all internal coefficients Ai can be expressed through Bi coefficients as follows: A1 = − p1 B2 ,

A2 = −b1 B2 ,

A3 = d 2 B2 − b2 B3 ,

A4 = 1 .

(10)

Thus, we have to find only three coefficients Bi , i = 2 − 4 , as B1 = 0 . After some algebra, we get the following downward recursion with the starting B4 value given below: Bi = ci Bi +1 , i = 2, 3 , B4 =

1 , d 3c3 − b3


(11)

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c2 =

p3 p2 , c3 = . b1 + q 2 b2 + q3 − d 2 c2

(12)

Equations (9)–(11) describe the external and internal fields in each layer, including the NM gap: ai3−1 Ei = Ai E0 + Bi 3 [3(E0rˆ )rˆ − E0 ] , rˆ = r / r , i = 1 − 4 . r

(13)

To evaluate the internal and external field enhancements, we use the field intensity averaged over a particular spherical surface S located within the gap, 2

〈 Ei 〉 s =

1 2 E i dS . ∫ S s

(14)

A similar figure of merit has been proposed for the external filed enhancement. 28 After simple calculations, we get 2

2

〈 Ei 〉 s = Ai + 2 Bi

2

ai6−1 , i = 1 − 4, rs6

(15)

where ai −1 ≤ rs ≤ ai . In our simulations (see below), the radius rs was equal to the core radius plus one half of the gap g , rs = a1 + g / 2 . Another useful quantity can be the gap field intensity averaged over the total gap volume Vg

2

〈 Ei 〉Vg

ai3 3 2 = Ai + Bi , 2 (ai + g )3 2

(16)

where, for a three-layered particle, the index i equals 2 for the gap and 4 for the external medium. In the latter case, the averaging volume is assumed to be V4 g = (4π / 3) (a4 + g )3 − a43  . Similar simple expressions can be obtained for the radial component of the local field, which can be more relevant for SERS experiments.28 To evaluate the accuracy of DA, we modified the multilayered Mie (ML Mie) solutions19,20 to 2

2

calculate the internal field in the gap and the averaged quantities 〈 Ei 〉 s and 〈 Ei 〉Vg . In all ACS Paragon Plus Environment


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simulations, the spectral dependence of the Au optical constants was calculated with a spline by using the FORTAN subroutine described in Section S4 (Supporting Information). It should be emphasized that the evaluation of SERS enhancement in terms of the known four-power law of the local field Eloc

4

holds within the small-particle electrostatic limit only29 but involves several

physical assumptions in the general case of electromagnetic interaction between a plasmon particle and a Raman molecule. For details, the readers are referred to works by Kerker et al.29 and Ausman and Schatz.30 Nevertheless, the published data30,31 show that the use of a plane wave approximation and the neglect of the interaction between gold or silver sphere and Raman dipole lead to small errors unless the particle size exceeds 50 nm. 2

Figure 10 shows the spectra of the surface-averaged field intensities in the hollow gap 〈 E g 〉 s of a 2

three-layered gold NM and the near-field intensity 〈 E4 〉 s . The NM radii of 7.5, 8.5, and 25 nm are close to the average parameters of the 15CIT-NMs. The surface-averaged intensity spectrum in the gap has a minor peak near 524, corresponding to the extinction plasmon resonance (Fig. 9c), and major peaks at 812 nm (DA) and 820 nm (ML Mie). Table 1 summarizes the averaged and maximal intensities from the DA and ML Mie calculations. By contrast with the near-field intensity, the gap intensity is two orders of magnitude stronger and is red shifted to 812–820 nm, quite far from the major extinction and scattering plasmon resonances of 524 nm but close to the minor resonance near 820 nm (Fig. 9c). It should be noted that a quantum-corrected model6 (QCM) does not predict the secondary classical electromagnetic far-field peaks. In our opinion, the appearance of a strong internal-field peak near 800 nm in Fig. 10a is not intrinsically related to the fairly minor far-field peaks near 820 nm. Moreover, the peak in Fig. 10a is in qualitative agreement with the measurements of SERS responses for different 2

wavelengths.1,6 Therefore, one can assume that the 〈 E g 〉 s spectra in Fig. 10a describe the internal plasmonic properties correctly and would retain their principal shape even after QCM correction.


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2

Figure 10. Spectra of the surface-averaged field 〈 E g 〉 s in the gap (a) and near a three-layered gold 2

NM 〈 E4 〉 s (b; the index i = 4 stands for the external medium), as calculated by DA (Eq. (14)) and by the ML Mie solution. The NM radii are 7.5, 8.5, and 25 nm; the refractive index of the gap medium was set to be 1.4; and the averaging sphere radius was rs = a1 + g / 2 for the gap and rs = a3 + g / 2 for the external field. Panel (c) shows the spectra of the far-field extinction and scattering efficiencies, Qext and Qsca , respectively (the integral optical cross sections normalized to the geometrical cross sections). Surprisingly enough, the quite simple equation (14) reproduces exact multipole calculations by ML Mie with reasonable accuracy. The maximal relative error of DA is about 27 % near 530 nm. Similarly, the near-field intensity by DA is about 25 % lower than that from the ML Mie calculations. The extinction and scattering spectra in Fig. 10c predict minor peaks near 820 nm, which are not seen in the experimental spectra. This disagreement between classical electromagnetic simulations and experimental measurements have been explained in terms of a QCM that replaces the NM gap by an effective medium with tunneling conductance to account for electron tunneling across the subnanometer dielectric gap.32 On the other hand, this minor peak can be simply washed out by the size and shape polydispersity of experimental samples. It is well known that the SERS response from a plasmonic substrate depends mainly on the electromagnetic hot spots, rather than on the average local-field intensity.33 To address this point, we calculated the spatial distributions of the local electromagnetic field in the gap and near the outer NM



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surface. For illustrative purposes, only the equatorial (x, y) plane was considered, with the incident electric field being directed along the x-axis (Fig. 11). In general, both the ML Mie and the approximate DA calculations give similar dipolelike distributions of the internal and near-field intensities, although the relative DA errors are somewhat higher than those for the surface-averaged intensities. For example, according to Table 1, the DA overestimates the maximal internal intensity in the gap by 37 % and underestimates the maximal near-field intensity by 15 %.

Figure 11. Distributions of the internal and external field intensities calculated for an NM with radii 7.5, 8.5, and 25 nm by DA (a) and by the ML Mie solution (b) at the wavelength 785 nm. The geometrical and material parameters of the NM correspond to those in Fig. 10. The incident field is propagated along the z-axis and is polarized along the x-axis (see picture in the bottom). The radius vector r (r , θ , ϕ ) lies in the equatorial plane (x, y) at θ = π / 2 , and the azimuth ϕ varies between 0 and π by

virtue of symmetry. The maximal intensity of the gap field is two orders of magnitude stronger than that for the near field around the particle.


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Table 1. Comparison of the averaged and maximal field intensities in the gap and near the surface of an

NM with radii 7.5, 8.5, and 25 nm. Calculations by DA and ML Mie theory. Parameter

Field intensities at 785 nm

Theory

〈 Eg 〉 s

〈 E4 〉 s

DA

293

3.34

1150

ML Mie

214

2.80

839

2

2

Eg

Major spectral peaks 2 max

2

2

2

〈 E g 〉 max / λmax s

〈 E4 〉 max / λmax s

10.8

864 / 812

14.9 / 528

12.7

848 / 820

19.5 / 534

E4

max

Figure 12 represents the radial distribution of the surface-averaged internal field in the gap and the near field around the NM. First, in agreement with the previous calculations, the surface-averaged field intensity in the gap is two orders of magnitude higher than that near the outer shell. Second, for a Raman molecule-sized distance of about 1 nm, the outer surface-averaged near-field intensity is almost constant and varies between 4.2 and 3.8. By contrast, the surface-averaged internal-field intensity in the gap decreases from 285 to 168.

Figure 12. Surface-averaged field intensity in the gap (1) and near the NM (2) as a function of distance from the core and the outer NM shell, respectively. Note the two orders of magnitude difference between the ordinate scales. ACS Paragon Plus Environment


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4.2. FDTD simulations of NMs with hollow and bridged gaps To explain the observed differences between the SERS spectra of the NMs with hollow and bridged gaps (Figs. 6 a,c and Figs. 6 b,d , respectively), we performed FDTD simulations for three NM models shown in Fig. S5, in some analogy with the simulations by Lim et al.1 and by Oh et al.12 Specifically, we considered NMs with a spherical hollow gap, spherical bridged gap, and polygonal bridged gap. Other details are indicated in Figure S5. The simulation results are shown in Fig. 13. Evidently, the field amplitude in the spherical bridged gap is stronger that that in the hollow gap. On the other hand, the field enhancement for polygonal bridged gaps was somewhat lower. This can be explained by strong dependence the field in the gap on the gap thickness (data not shown). The ratio between the maximal amplitudes in bridged and hollow gaps is in qualitative agreement with the experimental measurements.

Figure 13. Calculated internal and near-field distributions for NMs with 1-nm hollow spherical gap (a), bridged spherical gap (b), and bridged polygonal gap (c). Here, we assumed the gap to be filled with a dielectric medium (refractive index, 1.40) and with Raman BDT molecules. The external medium is water, and the incident wavelength is 785 nm. The electric field is directed along the x-axis. It should be emphasized that the internal field in the gap depends strongly on the NM structure and on the incident wavelength. For instance, 3D finite-element calculations by Lim et al. 1 gave comparable internal gap fields for (10, 11.2, 22) NMs with a bridged gap and for silica-insulated core–shell NMs with the same dimensions at 514 and 785 nm. However, they obtained an almost one order of magnitude difference between the field amplitudes at 633-nm excitation. Similar results have been reported by Oh ACS Paragon Plus Environment

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et al.12 They used a 3D FEM to simulate the internal filed for a (10,11.2, 21.2) gold NM with two sectorial hollow gaps. The arc angle of the interior bridged gap was gradually widened from 15 to 120 degrees. For 633-nm laser, the maximal field ratio between hollow and bridged NMs was about 3 for arc angles between 60 and 90 degrees. In contrast, for 514-nm laser, the authors observed weaker enhancement about of 1.6 for smaller arc angles about of 15 degrees. We have performed extensive ML Mie and FDTD simulations to correlate the electromagnetic SERS properties of the NMs with their structure and the excitation wavelength. These results are out of the scope of this article and will be discussed elsewhere.

Conclusions In this work, we have used seed-mediated growth to fabricate NMs with hollow and nanobridged gaps filled with BDT Raman molecules. The structure of the NMs and nanogaps inside them has been found to be different for smooth citrate-stabilized and polygonal CTAC-stabilized cores. In the first case, the growth of a secondary Au shell resulted in the formation of a subnanometer hollow interior gap containing BDT molecules. In the second case, the Au shell growth on the polygonal CTAC-stabilized Au cores yielded NMs with small bridged gaps and, for the smallest, 23-nm cores, nanomushrooms with incomplete outer shells. SERS experiments with two types of NMs with two core sizes, together with SERS experiments with BDT-functionalized cores, have led us to the following conclusions: (i) The major SERS peaks of the 23CTAC-NMs and 35CTAC-NMs at 1064 cm-1 are an order of magnitude higher than those for their 15CIT-NM and 35CIT-NM counterparts; (ii) the SERS responses from the BDT molecules located in a plasmonic NM gap are about an order of magnitude stronger as compared to the SERS signals from the BDT molecules located on the surface of the same cores and excited by an external plasmonic near-field; (iii) the SERS response from the NMs depends on the core size and gap thickness. Specifically, the ratio between the major peaks for NMs with large (35 nm) and small (15 nm, 23 nm) core sizes is about two for both NM types (with hollow and bridged gaps); and (iv) the SERS intensity of the major peaks of the 35CTAC-NMs at 1060 cm-1 is about an order of magnitude higher ACS Paragon Plus Environment


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than the peak intensities detected with the other three types of surface-functionalized nanoparticles, whose SERS enhancement increases in the following order: Ag cubes, Au@Ag nanorods, and Au nanostars. The above experimental observations have been correlated to electromagnetic simulations based on the developed simple DA theory, ML Mie, and FDTD calculations. There are several interesting points to be addressed in future studies. First, it would be desirable to accurately separate the electromagnetic mechanisms of enhancement by bridged NMs from possible variations in the number of excited Raman molecules. The most challenging issue is to verify the spectral dependence of the major SERS peaks and their dependence on the core size, gap thickness, or, generally speaking, NM structure. Again, the main difficulties stem from the uncertainty in the number of Raman active molecules and, additionally, from the difficulties associated with the precise control for NM size and structure. The second important point is the experimental and theoretical justification of the spectral peak for 2

〈 E g 〉 s obtained in this work (Fig. 8a). As this peak is in qualitative agreement with measurements of SERS responses for standard SERS wavelengths of common devices, we assumed that the spectra in Fig. 9a would give a reasonable physical picture and would retain their behavior even after QCM correction. This point, however, needs additional study. The next important point is related with applicability of classical electrodynamics to NMs with internal gap about 1 nm or less. It has been shown that QM model6 treats the quantum tunneling effects in terms of modified optical constants of the gap. In this sense, QM correction can be implemented in our simple DA as well as in more rigorous ML Mie simulations. To conclude, we hope that the experimental data and theoretical consideration in terms of a simple and instructive DA approximation can aid in the rational design and optimization of new NM “SERSinside” platforms.


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Supporting Information Available. Detailed information about the parameters of the as-prepared seed cores (Section S1, Figure S1, and Table S1); HRTEM and electron diffraction data for the 15CIT-NMs, including the determination of the interplane distances of the Au lattice fringes, corresponding to different Miller indexes, and related equations (Section S2, Figures S3 and S4, and Table S2); models for the NMs with hollow and bridged gaps used in FDTD simulations (Figure S5); spectral dependences of the real and imaginary parts of the bulk refractive index of Au, as calculated by a spline and compared with six sets of the experimental data found in the literature (Figure S6); FORTRAN codes for an illustrative program that launches a FORTRAN subroutine to calculate the interpolation spline parameters and the bulk or size-corrected optical constant of the gold nanoparticles for the spectral range 230–1610 nm.

Acknowledgements This research was supported by the Russian Scientific Foundation (project no. 14-13-01167). We thank D. N. Tychinin (IBPPM RAS) for his help in preparation of the manuscript and Drs. A. M. Burov and V. A. Khanadeev for help in TEM analysis.

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