Interaction between Nanoprisms with Different Coupling Strength

Article pubs.acs.org/JPCC

Interaction between Nanoprisms with Different Coupling Strength Michał Kotkowiak,* Bartłomiej Grześkiewicz, Elzḃ ieta Robak, and Eryk Wolarz Faculty of Technical Physics, Poznan University of Technology, Piotrowo 3, 60-965 Poznań, Poland S Supporting Information *

ABSTRACT: The aggregated noble metal system, consisting of two or more nanoparticles, possesses unique optical properties. The most important is the ability to generate larger local electric field enhancement than a single particle. In this work, we have modeled the system composed of silver nanoprisms with different geometries. For this purpose, the optical properties of the single silver nanoprism and the aggregated nanoprism dimer with adjacent and coplanar bases configuration have been studied by the finite integration technique. The relationship between the geometrical parameters, in particular the radius of the edges of curvature of a single nanoprism, and the position of the extinction peak has been described in a form of a mathematical equation. By moving and rotating one of the nanoprisms relative to the other in the dimer system, the coupling strength between them has been investigated by analyzing the nearfield and far-field properties. On the basis of these results, a hybridization model of the nanoprism dimer has been proposed. Our theoretical considerations presented in this article can be a useful tool for predicting the optical properties of the organized metal nanoparticles and the optimization of the assembly process.

1. INTRODUCTION One of the promising plasmonic structures is the nanoparticles with shapes different than spherical. The symmetry breaking in the shapes other than spherical leads to the appearance of a new absorption band, where the position and intensity of the maximum depend on the type of the excited electromagnetic modes.1 Especially interesting are these particles with the triangular-like particle shape, called nanoprisms or nanoplates (NP).2,3 NPs can be synthesized in the form of a nanoparticle or can be fabricated in the form of nanostructures with welldefined mutual distances and orientation.4−9 Because of the NP’s unique optical properties, e.g., a strong electric field enhancement on the tip, they have already found an application in the surface-enhanced Raman spectroscopy (SERS) and the plasmonic solar cell construction.10 The system, consisting of two or more plasmonic nanoparticles, can generate a larger local field enhancement than a single particle due to the hot spots present between their junctions.11 Additionally, if the particle contains sharp tips, the lightning rod effect can occur.5,11,12 The simplest model of a coupled plasmon system (nanoparticle aggregate) is a dimer in which two particles are closely packed. Understanding the mutual interaction between the aggregated nanoparticles is an up-to-date topic and the subject of much interest.5,9,11,13,13−21 The interactions can be roughly divided into the weakly and strongly interacting regimes depending on the nanoparticle orientation and their mutual distance. From all the previous studies the lack of the research concerning NP aggregates can be observed,5,13 although it is crucial to understand the mechanism of the assembly and formation of superlattices. Various types of the extinction bands were observed and reported for noble metal NPs in the surface plasmon resonance © XXXX American Chemical Society

spectra. The most intense band corresponds to the in-plane dipole resonance.22 Multipolar resonances are also observed, but they do not influence the overall effect strongly.22−24 Furthermore, higher-order resonances are perturbed when the realistic, rounded NP geometry has been taken into account because of the charge spread out at the rounded tip. Therefore, a lot of attention is paid to the dipole in-plane resonance and its connection with the NP structure.25 In this paper, the extinction cross section (ECS) spectra, the electric near-field enhancement (EFE) distribution maps, the electric field enhancement factors (EFEF), and the mean electric field enhancement (MEFE) of the aggregated silver (Ag) NP dimer with rounded tips were simulated by the finite integration technique (FIT). The coupling strength for all the analyzed NPs was controlled by varying the distance between the NP in the coplanar bases system for a different orientation angle. This allowed studying the influence of coupling on the optical properties of two triangular NPs (NP dimers). The plasmon hybridization model, which is strongly dependent on the distance (results in the near-field interaction), was proposed for the NPs in the dimer.21 The calculation of all the above-mentioned physical parameters and the proposed model have provided an intuitive approach to study the influence of the random distribution of the Ag NPs on the optical properties of the system. Received: December 8, 2014 Revised: February 25, 2015

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DOI: 10.1021/jp512220e J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Configuration of a single nanoprism (φ = 0°) and the incident light vectors applied for all the configurations (a), the system of nanoprisms with adjacent bases (φ = 30°) (b), coplanar bases with the edge−tip configuration (n = 2, φ = 0°) (c), and coplanar bases with the tip−tip configuration (n = 2, φ = 0°) (d).

Figure 2. Wavelength of the ECS maximum versus i-factor (a) and intercept factor f versus edge length L (b). The data are for m = 3.

2. MATERIALS AND METHODS The schematic Ag NPs with a different alignment are shown in Figure 1. Figure 1a shows a single Ag NP with rounded edges being a part of the aggregated structures presented in Figure 1b−d. The radii of the edge curvatures were obtained by inscribing the circle of radius R into the edges and replacing the segments forming the edges with arcs of radius R. Figure 1b shows the systems with adjacent bases of two bonded NPs with the interparticle distance equal to 0 nm, where the top NP can be rotated with respect to the bottom one by the angle φ. The angle φ is measured between the direction of an incident light polarization and the height of NPs. The height of the upper NP is parallel to the light polarization. By definition, φ is measured counterclockwise. Figure 1c and Figure 1d show the system of NPs with coplanar bases in the edge−tip and tip−tip configuration, respectively. By convention, in the numerical simulations the right NP is rotated with respect to the left one by the angle φ. The degree of the aggregation and, consequently, the coupling strength were controlled by changing the mutual distance between the NP centers and the φ angle in the range from 0 to 60° for the edge−tip configuration and from 0 to 45° for the tip−tip configuration. The normalized distance parameter n is introduced for the edge−tip configuration (Figure 1c) as n = (l/15√3) and for

the tip−tip configuration (Figure 1d) as n = (l/20√3), where l is the distance between geometrical centers of the NPs. The distance parameter n varies in the range between 0 and 3. For n = 2, in both configurations where φ = 0°, the NPs almost come into contact with each other. In the first approach, the impact of changing the dimensions of single Ag NPs on the ECS spectra was examined, and next, the dimensions of Ag NPs were fixed. The edge length L and the thickness T of the NPs were equal to 60 and 10 nm, respectively. All the analyzed systems of the NPs were illuminated from the top. The wave vector of the light wave was perpendicular to the plane in which NPs were placed. The incident light was polarized linearly along the heights of the triangle or the section joining the centers of the NPs as shown in Figure 1. Numerical simulations were performed by employing the finite integration technique (FIT) implemented into the CST Microwave Studio software (www.cst.com). A deeper insight into this method was described elsewhere.25 All the simulations presented in this paper used a frequency domain solver with a tetrahedral mesh. The tetrahedral grid provides flexibility in approximating arbitrary (rounded) geometries.26 We have used a tetrahedral mesh of about 450 000 cells. The grid step varied from 0.5 nm inside the NP to 10 nm in the free space. B


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A series of simulations with various i and m factors allowed to us generalize eq 4 and adjust its coefficients. This dependence is described by the equation which has not been reported in the literature previously

The FIT method was used to calculate the ECS spectra, the EFE (given by the ratio |E|/|E0|, where |E0| is the magnitude of the incident field and |E| is the magnitude of the local electric field), and also the EFEF and the MEFE values. EFEF is defined by19 ⎛ |E | ⎞ EFEF = ⎜ ⎟ ⎝ |E 0 | ⎠

max λECS = ai + (bL + cd m − 3)

4

Here a (−11.30 ± 0.46) nm, b (0.61 ± 0.01), and c (466 ± 7) nm are the parameters which follow from linear regression (Figure 2a), and d = (1.05 ± 0.01) is a parameter introduced to take into account the dependence on the T in eq 5. To demonstrate the applicability and the evidence of eq 5, additional data for m equal to 4, 5, and 6 are presented in the Supporting Information (see Figure S1). The dependence of the ECS maximum wavelength given in eq 5 creates the possibility to engineer and control the wavelengths (frequency) at which the plasmon resonance occurs for the Ag NPs by altering their geometrical structure. It has recently been shown that structures in cofacial arrangement can be orientationally controlled.29−31 For the configuration with the adjacent bases of NPs (Figure 1b), the ECS spectra were calculated for different φ angles. The results are presented in Figure 3. Additionally, the ECS spectra for an

(1)

and it was probed at a hot spot between NPs (the point where the electric field had a maximum value). The MEFE is described as k

MEFE =

l

|Eij|

∑i = 1 ∑ j = 1 |E | 0

kl

(2)

where k and l are the indices of a particular cell in the mesh and Eij is the magnitude of the local electric field in a given cell. The MEFE was calculated by averaging EFE over all accessible Ag NP surfaces.

3. RESULTS AND DISCUSSION Numerical analysis of the influence of the edge length L and radius of the edge curvature R and the nanoparticle thickness T of a single Ag NP on its optical properties is presented in Figure 2. For convenience, the tip and thickness proportional factors i and m, respectively, were introduced as follows i = 60 m=

(5)

R L

L T

(3)

In our case, we analyzed the cases of m = 3, 4, 5, and 6 and i less than 3. As it could be expected, the ECS spectra (results not shown), which consist of both absorption and scattering from the NPs, are represented by the symmetric curves with one distinct maximum. The maximum is assigned to the in-plane localized surface plasmon resonance (LSPR) modes. The ECS spectra maximum position and the value at ECS maximum (results not shown) increase with the increasing NP edge length L, which is a well-known phenomenon described in the literature.27,28 To investigate the influence of geometrical parameters (L, R, and T) on the optical properties of NPs, a versatile analysis has been performed. In Figure 2, only exemplary results for m = 3 are shown. Figure 2a shows the relation between the wavelength of the ECS peak position and the i-factor for various L. As can be seen, the wavelength of the ECS peak maximum versus i-factor is a linear function. For all the considered L (Figure 2a), the slope factor a is constant within the calculation error. Furthermore, the increase of the i-factor results in a blueshift of the ECS peak maximum. The reason for this phenomenon has been discussed previously.25 Results shown in Figure 2a can be fitted using the linear equations max λECS = ai + f

Figure 3. ECS spectra of the NPs with adjacent bases presented in Figure 1b for a different φ angle (solid lines), for a single NP (black dashed line), and for star-like structure (red dashed line). The EFE distribution maps of these systems are shown.

individual Ag NP (Figure 1a) and for the star-like structure are shown. The ECS peak for a single NP corresponds to the dipole resonance of the individual structure and results from the symmetry breaking.32 The NP has a 3-fold symmetry about the wave vector, and therefore, the rotation of the polarization plane has a negligible effect on the height, position, and shape of the ECS peak (results not shown). In the case of the star-like structure (the two NPs melted together), the charge in this system is localized symmetrically, similarly to the case of a single NP, and the increase in the ECS intensity is observed. However, for the adjacent configuration, when one NP is placed on the other (Figure 1b) and for φ = 0°, simultaneously (a case where the two NPs lie on each other) one peak blueshifted with respect to the single NP and the star-like structure, resulting from the aggregated system, is observed. For φ = 30° and φ = 60° an additional peak appears, which is redshifted in comparison to the peak of the single NP and star-like structure. If φ decreases, the higher frequency peak is shifted toward shorter wavelengths. However, the less intense, lower frequency peak is shifted toward longer wavelengths. Shorter

(4)

where a is the slope factor and f is the intercept factor (the ECS peak maximum position for i = 0) evaluated for results shown in Figure 2a. Figure 2b shows f-factor versus L for m = 3 evaluated for results shown in Figure 2a. As can be seen, f-factor is a linear function of L. C


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Figure 4. ECS spectra for the NPs in the edge−tip configuration for various angles φ and distance parameter n (a−e) and for various angles φ and at a constant distance between the closest parts of NPs, equal to 2 nm (f). The spectrum for a single NP is multiplied by 2.

simulations showing the influence of the distance parameter n and the φ angle on the ECS spectra were performed. Results for the edge−tip configuration and for the tip−tip configuration are shown in Figures 4 and 5. In both cases, the redshift of the CO peak is observed in comparison to the SO peak for the single NP.33 The near-field coupling is strongly dependent on the distance between particles, and the redshift increase with the decrease of the distance parameter n is observed. Moreover, changing the orientation of one of the NPs entails variations in the distance between the NPs. This is also manifested by the redshift of the peak connected with the CO mode (Figure 4a− d). In theory, the near-field coupling strength is inversely proportional to the third power of the distance between particles.17 The results presented in Figure 4 show that the redshift of the CO peak in the ECS spectra occurs when the distance between the NPs decreases, regardless of the φ angle. The redshift of the CO peak is the greatest for the case n = 2 and simultaneously φ = 0°. In the case of a constant distance

wavelength peaks of the aggregates represent a typical dipole resonance which occurs in the single NP. The red-shifted peaks, which appear during the NP rotation, are due to the accumulation of the part of the surface charge in the face-toface gap region between the top and the bottom NPs (see the EFE distribution maps in Figure 3). The additional maximum for φ = 0° is not present, which is due to the strongest NP coupling. Another common way of self-organization of the metal NP presented in the literature7,8 assumes that the aggregated system has a coplanar bases configuration (Figure 1c,d). When the two NPs are close enough, the plasma oscillations in the separate NPs interact with each other. Therefore, the individual NP experiences not only the field of the incident light but also the near field from the particle next to it. Then, the separate oscillations of electrons in the individual NP (SO mode) or the collective oscillations (CO mode) are excited, respectively. As a result, the change in the LSPR peak position for the aggregates is observed.17,33 To check this observation, the numerical D


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Figure 6. Wavelength of the ECS maximum (left axis filled symbols) and the ECS peak maximum value (right axis opened symbols) versus φ angle for the edge−tip configuration (black and red symbols) and for the tip−tip configuration (blue symbols). For the edge−tip, the data for CO mode (square black symbols) and for SO mode ECS peaks (circle red symbols) and for the tip−tip the CO mode ECS peak (triangle blue symbols) are presented. The distance parameter n is equal to 2.

Theoretically, bringing the particles close together may cause the excitation of higher multipolar plasmon modes (quadrupole and higher), with the maximum of the ECS spectra shifted toward the shorter wavelengths compared to the dipole modes.18,23,34 The presence of higher-order plasmon modes should be further investigated.23 The ECS maximum for the SO mode (Figure 4) can be assigned to the dipole LSPR of a single NP (weak coupling). Also, the ECS maximum for the CO mode exhibits the dipole-like character related with the ECS maximum shift toward lower energy.35 In the case of the tip− tip configuration only one dipole resonance (CO mode) is observed (Figure 5), which results from the strong coupling between the tips of the NPs. To recognize the type of the resonance, the EFE distribution maps and the polarization E vectors for the distance parameter n = 2 and the various φ are shown in Figure 7 and in Figure S2 (Supporting Information), respectively. On the basis of the EFE distribution maps and the polarization E vectors, the presence of the higher-order multipoles cannot be confirmed.19 The absence of the higher modes was noticed when the edges of the NPs were rounded.35 These observations can be useful for describing the real NP geometries which are important for plasmonic devices.23,25 Increasing φ leads to the more separated system and to the increase in the asymmetric oscillation of the surface charge. Then the coupling strength is reduced. In the edge−tip configuration (Figure 4), for small distances parameter n, two distinct peaks in the ECS spectrum are found for φ from 0° to 45° (the SO and the CO modes). Both peaks represent the dipole resonance, which is confirmed by the EFE distribution maps (Figure 7a−h). The EFE distribution maps also reveal that for the SO mode the coupling is very weak, whereas for the CO one the coupling becomes stronger. The coupling between the NPs is almost not observed for φ = 60° (Figure 7i), which is manifested in the ECS spectra (Figure 4e). In the case of the tip−tip configuration (Figure 7j−m), the coupling strength is so strong that the movement of the surface charge is completely dominated by the dipole−dipole interaction between the NPs (single peak in the ECS spectra). The charge is localized mostly on the tips of the NPs, and thus the EFE is greater for the tip− tip configuration than for the edge−tip due to the coupling between the particles.

Figure 5. ECS spectra for the NPs in the tip−tip configuration for φ = 0° (a) and φ = 15° angles (b) for various distance parameters n. The spectrum for a single NP is multiplied by 2.

between the NPs, the results are presented in Figure 4f. It can be seen that the redshift of the CO and SO peaks increases with the increase of the φ angle. Moreover, the intensity of the CO peak decreases, and the intensity of the SO peak increases with the increase of the φ angle. In Figure 5 the ECS spectra for the tip−tip configuration for two given angles, φ = 0° and φ = 15°, are shown. These two angles were chosen based on the spectra included in Figure 4 because for these two angles the coupling between the NPs was the strongest. The results show only one maximum in the ECS spectra. In this case, the shift of the maximum of the CO peak toward lower frequency is observed, similarly to the edge−tip configuration. This effect is the most evident for φ = 0° (Figure 5a) since the interactions between surface plasmons of the individual NPs are the strongest for that mutual orientation of the individual NPs. For a clearer view of the edge−tip and the tip−tip case, the dependence between the wavelength of the ECS maximum versus the φ angle for the CO peak (lower frequency) and for the less intense SO peak (higher frequency) at a constant distance parameter (n = 2) is presented in Figure 6. For the edge−tip configuration, the maximum value of the ECS peak of the SO mode increases systematically, whereas this value of the CO peak decreases with the increase of the φ angle. For the tip−tip configuration, the ECS peak maximum value of the CO mode also decreases with the increasing φ angle. At φ = 30°, the values of the ECS maxima for both configurations have comparable values. The more the particles become separated, the more both observed peaks (SO, CO) for the system move toward the peak for a single NP. E


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Figure 7. EFE distribution maps for the NPs in the edge−tip (a−i) and the tip−tip (j−m) configurations at the wavelengths corresponding to the maxima. The distance parameter n is equal to 2.

electric field between the NPs cannot be treated as a linear function of the distance between the particles. The EFEF is stronger for the tip−tip configuration than for the edge−tip configuration. The MEFE values were calculated for various φ angles. The results are presented for the edge−tip and the tip−tip configurations in Figure 9. For both cases, only the CO peaks in the ECS spectra are shown (see Figures 4 and 5). In the case of the edge−tip configuration, the dependence of the MEFE on the distance parameter n for its lower values exhibits increasing characteristics for φ angles in the range from 0° to 45°. Due to the weak coupling between the NPs, the course of the curve for φ = 60° substantially differs from the other courses for smaller φ angles.27 Comparing the data with those in Figure 8 and in Figure 9, for the edge−tip configuration with the closest proximity of the NPs (n < 2.25), one can see an evident drop observed in both ECS peak maximum values (Figure 8). This effect is correlated with the MEFE (Figure 9) in the case of the edge−tip configuration excluding φ = 60°, for which coupling is not observed in the edge−tip configuration. For the edge−tip configuration and for the distance n parameter greater than 3.00, the MEFE values are almost constant regardless of φ. For the tip−tip configuration, the relation between the MEFE and φ is quite different than for the edge−tip system (Figure 9b). For n greater than 2.13, the MEFE value decreases

Finally, to get additional information about coupling strength for the edge−tip and the tip−tip configurations of the NPs, the logarithm of EFEF determined for the wavelength of the ECS maximum of the CO mode, probed at the point between the NPs (point on the plane of symmetry), as well as the ECS peak maximum value and the ECS maximum peak position were calculated as a function of the distance parameter n for φ = 0°. The results are presented in Figure 8. It is seen from Figure 8a that the ECS peak maximum value for the edge−tip configuration (CO mode) reaches its maximum for the distance parameter n greater than 2. This could suggest the interaction between NP modes, and thus, the energy of the exciton at the second NP is reduced. A similar phenomenon was reported previously for dimers of gold nanorods in the Tconfiguration.33 However, the described situation is not observed for the tip−tip configuration. This is probably due to the strong coupling between tips. Moreover, when the distance parameter n increases, the coupling strength decays in an exponential way, which was also observed for the aggregated structures with small gaps in the previous work by McMahon et al.19 With the increasing distance parameter n, the CO peaks are shifted toward higher frequencies, and they are more and more similar to the SO peak observed for the case of the weak coupling between the NPs. The logarithm of EFEF shows the exponential dependence on n for both the tip−tip and the edge−tip configurations (Figure 8b), which means that the F


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Figure 9. MEFE parameter for CO modes versus NP distance parameter n for different φ angle for the edge−tip (a) and the tip−tip configuration (b).

Figure 8. Wavelength of the ECS maximum (left axis) and the ECS peak maximum value (right axis) evaluated for CO mode (φ = 0°) for the edge−tip configuration (filled and opened black squares, respectively) and for the tip−tip configuration (filled and opened blue triangles, respectively) (a) and a logarithm of EFEF for the edge− tip (black) and the tip−tip configuration (blue) (b) versus the distance parameter n.

with this parameter, which is the most evident for φ = 45°, and indicates that increasing the distance between NPs in the tip− tip configuration for φ = 45° affects the MEFE value the most and leads to the greatest drop of this value. However, for n lower than 2.13 and for φ = 0° and φ = 15°, the increase of the MEFE value with the increase of n, connected with the strong coupling, is observed. In the case of the tip−tip configuration, a characteristic cross point of the MEFE values at n = 3 is observed (the MEFE value has a very similar value for all the presented curves). For n = 3, the changes in φ have a meaningful effect on the MEFE values. If n is smaller than 3, the MEFE value increases with the φ angle, whereas for n greater than 3, the relation is reversed. The MEFE for φ = 0°, for the edge−tip and the tip−tip configurations, also obtains its maximum at a distance n > 2, and the ECS maximum peak value dependence (Figure 8) demonstrates descending characteristics regardless of the φ angle. To give the explanation of the plasmonic response of the NPs arranged in the edge−tip configuration at a constant distance between the closest parts of NPs equal to 2 nm, the hybridization model is presented in Figure 10 for the considered system. The plasmon hybridization theory suggests that the coupling in aggregates could be treated as a hybridization of plasmons in the nonaggregated structures by the analogy to molecular orbitals.36 The hybridization model is based on the charge distribution in the nanoparticles. The asymmetric charge distribution leads to the antibonding mode, while the symmetric charge

Figure 10. Plasmon hybridization energy diagram for the edge−tip configuration and for various φ angles at a constant distance between the NPs equal to 2 nm between the closest parts of the NPs for longitudinal (a) and transversal (b) light polarization. The negative and the positive charge signs give the qualitative information about the charge distribution (charge conservation principle is fulfilled for each structure). The antibonding and bonding modes are indicated by red and black colors, respectively. G


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Due to interference that occurs between the near fields for the coupled system and for the maximum of the electric field enhancement and the ECS maximum, the peak value is shifted for distances n > 2, the most evident for φ = 0−15°. These results demonstrate the importance of the detailed structural information in the single and aggregated nanoparticle studies. We have shown that the aggregations could disturb the projected device absorption profile when assuming that there are no aggregates at all. We believe the results described herein will have important implications in the design and choice of the metal NP geometry for applications which are focused on both far-field and nearfield optical properties.

distribution results in the bonding mode.21 The energy of the bonding mode is usually lowered when compared to the antibonding one.37−40 However, for more complicated systems (i.e., with broken symmetry), the antibonding mode can be observed at lower energy than the bonding mode.41 The energy levels shown in Figure 10 are placed in order of increasing energy and were obtained from additional calculations of the ECS spectra for the edge−tip configuration with the incident light polarized transversely (see Figure 4f and Figure S3 in the Supporting Information for the longitudinal and transverse light polarization, respectively). Transverse light polarization direction is defined as the direction at which the electric field of the incident wavelength is perpendicular to the section which joins the geometrical centers of the NPs. The charge distribution was determined based on the polarization E vectors (results are presented in Figures S4 and S5 in the Supporting Information). As a reference point to the charge distribution, the tips (or edges, for φ = 60°) of the NP that are located in the closest proximity of each other were chosen.41 The antibonding interactions are indicated by the red color of the state and the bonding interactions by the black one. On the basis of the charge distribution on the surface of the NPs, one could conclude that for the longitudinal polarization the antibonding modes are enhanced with the increasing φ. Also, their energy is lowered when compared to the noncoupled system. This could be connected with the decrease in the coupling strength between NPs while the angle φ is increased. For the transversal polarization the situation is quite different. In this case, only the bonding modes are observed regardless of the φ angle. Those modes are associated with higher energy of the hybridization and are characterized by the symmetric charge distribution on the surface of the NPs.

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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S5. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +48 665 3177. Fax: +48 665 3178. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Poznan University of Technology 06/62/DSMK/0192/2014. ABBREVIATIONS LSPR, localized surface plasmon resonance; NP, nanoprism; ECS, extinction cross sections; EFE, electric near-field enhancement; EFEF, electric field enhancement factors; MEFE, mean electric field enhancement; FIT, finite integration technique; SO, separate oscillations; CO, collective oscillations

4. CONCLUSIONS Understanding the relationship between the optical response of the aggregated noble metal nanoparticles is important to effectively design devices based on their plasmonic properties. We presented here a systematic study of the Ag NPs forming dimers interacting with different coupling strengths by changing the angle of the nanoparticle orientation and their mutual distances. For the single NP, we have observed that the position of the ECS peak is dependent substantially on the radius of the edge curvature. We have found that the position of the ECS peak maximum is a linear function of i-factor in studied radius of the edge curvature range. The slope of this linear dependence is approximately the same for the nanoprisms of various edge length, if the length to thickness ratio is fixed. The formula, which describes the wavelength of the ECS maximum for various Ag NP geometrical parameters, is proposed. Furthermore, three types of self-organization of the metal NP presented in the literature were also considered. For the system of the two NPs with adjacent bases, the decrease in matching of the nanoparticle results in the redshift of the ECS peak and band splitting. Due to the coupling effect, the new peak at a longer wavelength appeared. We have shown that for the system with coplanar bases the in-plane dipole resonance plays the main role in the optical response of all the Ag NP systems which is due to introducing the radius of the edge of curvature greater than zero. The ECS maximum localized in the blue part of the spectra can be assigned to the dipole resonance of a single NP, whereas the ECS maximum placed in the red part is due to the coupling between the aggregated NPs.

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REFERENCES

(1) Li, X.; Choy, W. C. H.; Lu, H.; Sha, W. E. I.; Ho, A. H. P. Efficiency Enhancement of Organic Solar Cells by Using ShapeDependent Broadband Plasmonic Absorption in Metallic Nanoparticles. Adv. Funct. Mater. 2013, 23, 2728−2735. (2) Ding, W.; Bachelot, R.; Kostcheev, S.; Royer, P.; Espiau de Lamaestre, R. Surface Plasmon Resonances in Silver Bowtie Nanoantennas with Varied Bow Angles. J. Appl. Phys. 2010, 108, 124314. (3) Duan, H.; Fernández-Domínguez, A. I.; Bosman, M.; Maier, S. A.; Yang, J. K. W. Nanoplasmonics: Classical down to the Nanometer Scale. Nano Lett. 2012, 12, 1683−1689. (4) Chen, L.; Ji, F.; Xu, Y.; He, L.; Mi, Y.; Bao, F.; Sun, B.; Zhang, X.; Zhang, Q. High-Yield Seedless Synthesis of Triangular Gold Nanoplates through Oxidative Etching. Nano Lett. 2014, 141124143028006. (5) Dreaden, E. C.; Near, R. D.; Abdallah, T.; Talaat, M. H.; ElSayed, M. A. Multimodal Plasmon Coupling in Low Symmetry Gold Nanoparticle Pairs Detected in Surface-Enhanced Raman Scattering. Appl. Phys. Lett. 2011, 98, 183115. (6) Aherne, D.; Ledwith, D. M.; Gara, M.; Kelly, J. M. Optical Properties and Growth Aspects of Silver Nanoprisms Produced by a Highly Reproducible and Rapid Synthesis at Room Temperature. Adv. Funct. Mater. 2008, 18, 2005−2016. (7) Ye, J.; Van Dorpe, P. Plasmonic Behaviors of Gold Dimers Perturbed by a Single Nanoparticle in the Gap. Nanoscale 2012, 4, 7205. H


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Excitation Wavelength on the Optical Properties. Chem. Phys. 2013, 423, 142−150. (28) Shuford, K. L.; Ratner, M. A.; Schatz, G. C. Multipolar Excitation in Triangular Nanoprisms. J. Chem. Phys. 2005, 123, 114713. (29) Kohlstedt, K. L.; Olvera de la Cruz, M.; Schatz, G. C. Controlling Orientational Order in 1-D Assemblies of Multivalent Triangular Prisms. J. Phys. Chem. Lett. 2013, 4, 203−208. (30) Jones, M.; Macfarlane, R.; Lee, B.; Zhang, J.; Yung, K.; Senesi, A.; Mikrin, C. DNA-Nanoparticle Superlattices Formed from Anisotropic Building Blocks. Nat. Mater. 2010, 9, 913−917. (31) Young, K. L.; Jones, M. R.; Zhang, J.; Macfarlane, R. J.; EsquivelSirvent, R.; Nap, R. J.; Wu, J.; Schatz, G. C.; Lee, B.; Mirkin, C. A. Assembly of Reconfigurable One-Dimensional Colloidal Superlattices due to a Synergy of Fundamental Nanoscale Forces. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 2240−2245. (32) Yu, Y.-Y.; Chang, S.-S.; Lee, C.-L.; Wang, C. C. Gold Nanorods: Electrochemical Synthesis and Optical Properties. J. Phys. Chem. B 1997, 101, 6661−6664. (33) Funston, A. M.; Novo, C.; Davis, T. J.; Mulvaney, P. Plasmon Coupling of Gold Nanorods at Short Distances and in Different Geometries. Nano Lett. 2009, 9, 1651−1658. (34) Rang, M.; Jones, A. C.; Zhou, F.; Li, Z.-Y.; Wiley, B. J.; Xia, Y.; Raschke, M. B. Optical Near-Field Mapping of Plasmonic Nanoprisms. Nano Lett. 2008, 8, 3357−3363. (35) Millstone, J. E.; Hurst, S. J.; Métraux, G. S.; Cutler, J. I.; Mirkin, C. A. Colloidal Gold and Silver Triangular Nanoprisms. Small 2009, 5, 646−664. (36) Prodan, E. A Hybridization Model for the Plasmon Response of Complex Nanostructures. Science 2003, 302, 419−422. (37) Handbook of Nanomaterials Properties; Bhushan, B., Luo, D., Schricker, S. R., Sigmund, W., Zauscher, S., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, 2014. (38) Batson, P. E.; Reyes-Coronado, A.; Barrera, R. G.; Rivacoba, A.; Echenique, P. M.; Aizpurua, J. Nanoparticle Movement: Plasmonic Forces and Physical Constraints. Ultramicroscopy 2012, 123, 50−58. (39) Kumar, J.; Wei, X.; Barrow, S.; Funston, A. M.; Thomas, K. G.; Mulvaney, P. Surface Plasmon Coupling in End-to-End Linked Gold Nanorod Dimers and Trimers. Phys. Chem. Chem. Phys. 2013, 15, 4258. (40) Sheikholeslami, S.; Jun, Y.; Jain, P. K.; Alivisatos, A. P. Coupling of Optical Resonances in a Compositionally Asymmetric Plasmonic Nanoparticle Dimer. Nano Lett. 2010, 10, 2655−2660. (41) Wu, S.; Zhou, L.; Wang, Q.; Zhang, X.; Zhu, Y. Hybridized Effects of Plasmonic Quadrupolar and Dipolar Resonances on the Perforated Planar Metallic Film. J. Phys. D: Appl. Phys. 2013, 46, 065302.

(8) Rosen, D. A.; Tao, A. R. Modeling the Optical Properties of Bowtie Antenna Generated By Self-Assembled Ag Triangular Nanoprisms. ACS Appl. Mater. Interfaces 2014, 6, 4134−4142. (9) Shao, L.; Woo, K. C.; Chen, H.; Jin, Z.; Wang, J.; Lin, H.-Q. Angle- and Energy-Resolved Plasmon Coupling in Gold Nanorod Dimers. ACS Nano 2010, 4, 3053−3062. (10) Stratakis, E.; Kymakis, E. Nanoparticle-Based Plasmonic Organic Photovoltaic Devices. Mater. Today 2013, 16, 133−146. (11) Camargo, P. H. C.; Au, L.; Rycenga, M.; Li, W.; Xia, Y. Measuring the SERS Enhancement Factors of Dimers with Different Structures Constructed from Silver Nanocubes. Chem. Phys. Lett. 2010, 484, 304−308. (12) Kessentini, S.; Barchiesi, D.; D’Andrea, C.; Toma, A.; Guillot, N.; Di Fabrizio, E.; Fazio, B.; Maragó, O. M.; Gucciardi, P. G.; Lamy de la Chapelle, M. Gold Dimer Nanoantenna with Slanted Gap for Tunable LSPR and Improved SERS. J. Phys. Chem. C 2014, 118, 3209−3219. (13) Zhou, Y.; Zhou, X.; Park, D. J.; Torabi, K.; Brown, K. A.; Jones, M. R.; Zhang, C.; Schatz, G. C.; Mirkin, C. A. Shape-Selective Deposition and Assembly of Anisotropic Nanoparticles. Nano Lett. 2014, 14, 2157−2161. (14) Tserkezis, C.; Taylor, R. W.; Beitner, J.; Esteban, R.; Baumberg, J. J.; Aizpurua, J. Optical Response of Metallic Nanoparticle Heteroaggregates with Subnanometric Gaps. Part. Part. Syst. Charact. 2014, 31, 152−160. (15) Grant, C. D.; Schwartzberg, A. M.; Norman, T. J.; Zhang, J. Z. Ultrafast Electronic Relaxation and Coherent Vibrational Oscillation of Strongly Coupled Gold Nanoparticle Aggregates. J. Am. Chem. Soc. 2003, 125, 549−553. (16) Jiang, M.-M.; Chen, H.-Y.; Li, B.-H.; Liu, K.-W.; Shan, C.-X.; Shen, D.-Z. Hybrid Quadrupolar Resonances Stimulated at Short Wavelengths Using Coupled Plasmonic Silver Nanoparticle Aggregation. J. Mater. Chem. C 2014, 2, 56. (17) Jain, P. K.; El-Sayed, M. A. Plasmonic Coupling in Noble Metal Nanostructures. Chem. Phys. Lett. 2010, 487, 153−164. (18) Atay, T.; Song, J.-H.; Nurmikko, A. V. Strongly Interacting Plasmon Nanoparticle Pairs: From Dipole−Dipole Interaction to Conductively Coupled Regime. Nano Lett. 2004, 4, 1627−1631. (19) McMahon, J. M.; Li, S.; Ausman, L. K.; Schatz, G. C. Modeling the Effect of Small Gaps in Surface-Enhanced Raman Spectroscopy. J. Phys. Chem. C 2012, 116, 1627−1637. (20) Kleinman, S. L.; Sharma, B.; Blaber, M. G.; Henry, A.-I.; Valley, N.; Freeman, R. G.; Natan, M. J.; Schatz, G. C.; Van Duyne, R. P. Structure Enhancement Factor Relationships in Single Gold Nanoantennas by Surface-Enhanced Raman Excitation Spectroscopy. J. Am. Chem. Soc. 2013, 135, 301−308. (21) Nordlander, P.; Oubre, C.; Prodan, E.; Li, K.; Stockman, M. I. Plasmon Hybridization in Nanoparticle Dimers. Nano Lett. 2004, 4, 899−903. (22) Yang, P.; Portalés, H.; Pileni, M.-P. Identification of Multipolar Surface Plasmon Resonances in Triangular Silver Nanoprisms with Very High Aspect Ratios Using the DDA Method †. J. Phys. Chem. C 2009, 113, 11597−11604. (23) Xu, X.-B.; Yi, Z.; Li, X.-B.; Wang, Y.-Y.; Liu, J.-P.; Luo, J.-S.; Luo, B.-C.; Yi, Y.-G.; Tang, Y.-J. Tunable Nanoscale Confinement of Energy and Resonant Edge Effect in Triangular Gold Nanoprisms. J. Phys. Chem. C 2013, 117, 17748−17756. (24) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment. J. Phys. Chem. B 2003, 107, 668− 677. (25) Grześkiewicz, B.; Ptaszyński, K.; Kotkowiak, M. Near and FarField Properties of Nanoprisms with Rounded Edges. Plasmonics 2014, 9, 607−614. (26) Weiland, T.; Timm, M.; Munteanu, I. A Practical Guide to 3-D Simulations. IEEE Microw. Mag. 2008, 9, 62−75. (27) Hermoso, W.; Alves, T. V.; de Oliveira, C. C. S.; Moriya, E. G.; Ornellas, F. R.; Camargo, P. H. C. Triangular Metal Nanoprisms of Ag, Au, and Cu: Modeling the Influence of Size, Composition, and I


Interaction between Nanoprisms with Different Coupling Strength

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