Article pubs.acs.org/JPCC
Plasmonic Coupling Effect on Spectral Response of Silver Nanoparticles Immobilized on an Optical Fiber Sensor Rani Dutta, Bhanu P. Singh, and Tapenendu Kundu* Department of Physics, Indian Institute of Technology, Bombay, Mumbai 400076, India S Supporting Information *
ABSTRACT: The localized surface plasmon resonance (LSPR) of silver nanoparticles during immobilization on the U-bent sensor fiber probe has been studied. The gradual wavelength shift of the peak resonance due to the increment of the number of nanoparticles on the fiber surface has been attributed to the plasmonic coupling effect. Since the immobilization is random, the shift of the resonance as well as the broadening of the absorption spectrum depends on the distribution of the nanoparticles. To get the insight of the cause of this spectral behavior, we have incorporated the two-particle coupling approximation and assumed that the particles form pairs with its nearest neighbors. The distribution of pairs was obtained from the microdimensional images of fiber surfaces. The collective response from the contributions of these pairs was calculated using the theoretical framework of discrete dipole approximation (DDA). The shifts of the resonance as well as the broadening of the calculated spectra were found to be in excellent agreement with those of the experimentally observed spectra. Thus, this methodology can be utilized for tuning and enhancing the sensitivity by exploiting the plasmonic coupling between the noble metal nanoparticles for designing and fabricating the LSPR based optical sensor.
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INTRODUCTION In recent years, a lot of attention has been paid on the development of sensors for various applications. Due to interdisciplinary efforts, new mechanisms and technologies have emerged to develop sensors with a high figure of merit.1−12 However, for practical applications, it is essential to have simple and flexible methodology which can be incorporated easily to make user-friendly, portable, and sustainable prototype devices for detection. Optical and spectroscopic detection techniques have been exploited immensely in this regard.3−5 Nowadays, the detections of biological and explosive molecules are of great interest due to its various applications in civil, defense, forensic, medicine, and military uses.6,7 Since detection and identification are the two most important criteria, extremely high sensitivity and selectivity are essential for the trace detection. Major effort is thus being made to develop optical sensor devices to increase the sensitivity and specificity. Since the localized surface plasmon resonance (LSPR) frequency of metal nanoparticle is very much susceptible to the dielectric constant of its environment, this phenomenon has been cleverly utilized to develop highly sensitive LSPR based chemical and biosensors.8−12 The resonance frequency of the localized surface plasmon of a nanoparticle varies with real part of the dielectric constant of metal which in turn depends on the size13,14 of the nanoparticle. Also, the interparticle interactions affect the resonant frequency of each particle due to the local field associated with the electronic oscillations of neighboring particles. This particle−particle coupling causes a peak shift in resonance with respect to that of the single particle. The © 2013 American Chemical Society
interparticle interactions of the metal nanoparticles have been studied by various research groups, both experimentally15,16 and theoretically.17−19 A red spectral shift of the plasmon resonance was observed for gold (Au) nanoparticles when the number of particles in a periodic array was increased.15,19 In another study, Storhoff et al.20 reported the red spectral shift for three-dimensional aggregate of Au nanoparticles. Recently, Zhang et al.21 showed that the interparticle interactions have significant effect on refractive index sensitivity for silver nanoparticle pair. Lange et al.22 have investigated the influence of size and interparticle distance on the plasmon coupling in the hybrid structure of gold nanoparticle and poly(Nisopropylacrylamide). Jain et al.23 have shown that the plasmonic nanoparticle pair exhibits higher sensitivity to the environment/medium refractive index as compared to an isolated nanoparticle. Recently we have reported24 the gradual red shift of the LSPR for different incubation time during immobilization of silver nanoparticles on the fiber core surface. Using single particle approximation in the framework of Mie’s theory, the observed red shift was attributed to the substrate effect as well as the departure from spherical symmetry of the electric field around the nanoparticles. The cause of this departure is the strong electromagnetic coupling between the randomly distributed nanoparticles on the fiber surface. For the development of LSPR based optical fiber sensor, several issues arise as regard to the sensitivity of detection Received: February 12, 2013 Revised: June 18, 2013 Published: July 17, 2013 17167
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mechanism. First, the sensitivity gets affected by the nature of surface chemistry which causes the random immobilization of nanoparticles on the fiber surface. Generally, one expects higher sensitivity with the increase of the number density of nanoparticles on fiber surface. But in this case, the LSPR resonance gets broadened due to the close interactions between the nanoparticles,25 and as a result, the sensitivity decreases. Second, the shift in absorption maximum depends on the interparticle spacing as well as polarization of the incident light.18,26,27 Gunnarsson et al.28 have reported the dependency of polarization of the scattered light from silver nanoparticle pair. When the polarized spectrum of scattered light was obtained along the direction perpendicular to the pair axis, a small blue shift was observed, whereas in a parallel polarization, a large red shift was monitored when interparticle spacing was decreased. In view of the issues discussed above, the polarization of the incident light, size, shape, and the density of the nanoparticles are crucial factors for optimizing the performance of a LSPR based optical sensors. This prompted us to pay attention to the collective LSPR response of the randomly distributed silver nanoparticles on the fiber surface. The motivation of our study is to understand the spectral shift and broadening mechanisms due to the interactions among these randomly distributed nanoparticles and to evolve a simple methodology that can be exploited for the development of the optical sensors. Here, we present our observations on collective LSPR of silver nanoparticles immobilized on the fiber core surface using evanescent wave absorption technique. The observed red spectral shift, as a function of particle distribution on the fiber surface, has been analyzed in the theoretical framework of DDA. This study may essentially provide insight into the possibility of enhancing the sensitivity of the fiber sensor by tuning the optical properties of randomly distributed silver/ gold nanoparticles.
Figure 1. Optical setup for monitoring evanescent wave based absorption spectrum. Xe: xenon lamp; MO: microscope objective; UFb: U-bent fiber probe; GCT: glass capillary tube for the incubation of the nanoparticle on fiber core; SP: fiber coupled spectrometer; DAC: data acquisition system. Inset shows the cartoon of silver nanoparticles (AgNPs) immobilized on the fiber core surface.
USA). The bent region of the fiber probe was held in a glass capillary tube (GCT) for the incubation of the nanoparticle on the fiber core surface. Light from the xenon lamp was focused using a microscope objective lens (MO), 40 × 0.4 NA, onto one polished fiber end. When the AgNP solution was introduced in the glass capillary tube, light emerging from the other end of the fiber was collected by the spectrometer (SP), and the absorption spectra of immobilized AgNPs on the fiber core surface at different incubation times were recorded.
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RESULTS AND DISCUSSION The UV−vis spectrum of AgNP in solution with absorption maximum at 425 nm is shown in Figure 2 (curve i). The AgNP solution was introduced into the glass capillary, and the absorption spectra were monitored by the spectrometer during the immobilization of AgNPs on the core surface of the sensor probe. In Figure 2, curves ii and iii show the absorption spectra of immobilized AgNPs of two different optical fiber sensor probes.
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EXPERIMENTAL SECTION Reagents and Materials. For the studies presented here, silver nitrate (AgNO3) and trisodium citrate (Na3C6H5O7) were obtained from Sigma and Aldrich chemicals, respectively. All of the reagents were of analytical grade. All solutions were prepared using deionized (DI) water obtained from a Milli-Q filtration system. Optical fibers of diameter 200 μm and NA = 0.37 were obtained from CeramOptec (201255 Optran HUV), USA. Synthesis of Silver Nanoparticle. Silver nanoparticles (AgNPs) used in these experiment were synthesized by following the procedure described by Lee et al.29 In this procedure, 1.05 mM (13.5 mg) of AgNO3 was added to 75 mL of DI water and heated to the boiling point under vigorous stirring. When the boiling started, a solution of 1% sodium citrate (1 mL) was added, and heating was continued for 1 h. The solution was removed from the hot plate and was cooled at room temperature. The solution prepared by this method was greenish yellow in color, and the maximum particle size distribution was found to be in the range of 60−70 nm. Optical Setup. Figure 1 shows the optical setup for monitoring evanescent wave based absorption spectrum of AgNPs during the immobilization on the fiber core surface. A silanized U-bent (length of the exposed fiber core of 1 cm) fiber probe (U-Fb) of bend radius 0.75 mm was prepared30 and placed between the broadband optical source (xenon lamp, Xe) and a fiber coupled spectrometer (SP, S2000 Ocean Optics,
Figure 2. Absorption spectrum of silver nanoparticle in solution (curve i). Absorption spectra of silver nanoparticle attached on the functionalized fiber core surface of first probe (curve ii) and second probe (curve iii). Arrows are the slope of (curve ii) and (curve iii) at 520 nm. 17168
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For the first probe, the absorption spectrum (curve ii) is having a single sharp resonance peak (λmax) at 434 nm. On the other hand, the absorption spectrum (curve iii) for the second probe consists of a peak at 441 nm with same optical density as the first probe and a shoulder at the higher wavelength region. The difference between these spectra arises from the variation of immobilization on the fiber surface which depends on the nature of surface chemistry. This variation may occur during the silanization process of fiber surface.30 In this process, the amine groups are created by dipping the fiber probes in silane solution prepared in ethanol and acetic acid mixture. The role of acetic acid is to maintain the orientation of amine groups of silane away from the surface and restricts the formation of multilayers of silane that could lead to the aggregation of nanoparticles. For a given LSPR absorption spectrum, the sensitivity can be defined as the rate of change of optical density (OD) with respect to wavelength at a given wavelength. As shown in Figure 2, the slope (ΔOD/Δλ) at wavelength 520 nm of curve ii is more than that of curve iii because of the broadening of curve iii. To understand this broadening, the distributions of the silver nanoparticles on these fiber surfaces were obtained by using a field emission scanning electron microscope (FE-SEM). Figure 3a and b displays the SEM images of small portion of
regard we have monitored the absorption spectra (Figure 4a, curves i−viii) of AgNP on a fiber sensor probe (probe a) at
Figure 3. Field emission scanning electron microscope (FE-SEM) images of distribution of AgNP on the fiber core surface of (a) the first probe and (b) the second probe. Figure 4. (a) Absorption spectra of silver nanoparticles attached on the functionalized fiber core surface at different incubation time. (b) λmax of the absorption spectra as a function of different optical density for six different probes: black ⬠, probe a; red ⬡, probe b; blue ☆, probe c; green ○, probe d; brown △, probe e; pink □, probe f.
AgNP immobilized fiber surfaces corresponding to curve ii and curve iii, respectively. Figure 3a reveals that the single absorption peak in curve ii appears due to isolated nanoparticles on the fiber surface. Figure 3b confirms that the absorption spectrum given in curve iii reflects the mixed signatures of isolated nanoparticles as well as the formation of clusters on the fiber surface. Since the nanoparticles are randomly immobilized, there could be two possibilities for the appearance of any resultant collective spectrum. First, the nanoparticles could be placed far from each other, and therefore the collective plasmon resonance would behave like a single particle response. Second, these nanoparticles could be situated close to other nanoparticles which would cause the spectral shift as well as broadening of spectrum due to the interactions between them.25 Also, they could form clusters which would produce the new band in the higher wavelength region of the spectrum. Therefore, we can say that two fiber probes may not have same sensitivity even though they have same optical density due to the variation of immobilization of nanoparticles. Thus the immobilization process is an important step for developing this kind of sensors for commercial applications. To decipher the role of interaction between randomly distributed nanoparticles, we have carried out systematic studies on AgNP distribution on the fiber core surface and its effect on the collective plasmon resonance absorption spectrum. In this
different incubation times. In this experiment it was observed that the λmax at optical density 0.68 (Figure 4a, curve i) was at 432 nm when the nanoparticles started to attach on the fiber surface. The red shift was approximately 7 nm compared to the solution spectrum. The intensity of the absorption peak increased and monotonically shifted further to red side from 7 to 21 nm (curve ii to curve viii) when the OD was increased from 0.68 to 2.6. Figure 4b shows the shift of peak resonance of probe a at different optical densities resulting from the increment of number of nanoparticles on the fiber surface. To analyze the effect of particle distribution at different intermediate steps, we have performed several experiments on various U-bent fiber sensor probes. From these experiments we have chosen only those fibers whose spectral behaviors were followed the same trend of dynamics as probe a. As presented in Figure 4b, probe b was stopped at optical density 2.3. Similarly probe c, probe d, probe e, and probe f were stopped at optical densities of 2.0, 1.65, 1.2, and 0.67, respectively. Figure 5 shows the final absorption spectra of these six sensor probes. In the inset, the variation of the peak resonance (λmax) of absorption spectra is plotted against optical density. 17169
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from the decrement of the interparticle distance. In this respect, considering the particle distributions are homogeneous, the average interparticle distances (dave = √[area of the SEM image/no. of nanoparticles]) were calculated from these SEM images. The dave were found to be 207, 264, 336, 442, 629, and 783 nm corresponding to optical densities of 2.6, 2.3, 2, 1.65, 1.2, and 0.67, respectively. Encina et al.25 have shown that for Ag nanoparticle pair, the particle−particle interaction becomes negligible when the interparticle distance is larger than 225 nm (as shown in Supporting Information, Figure 1S). In our observation, even when the dave is more than 225 nm, we observed the spectral shift. Therefore the analysis with average interparticle distance calculated from these SEM images does not provide adequate explanation for our observation. Lee et al.31 have discussed that the refractive index sensitivity depends on the surface density ratio of gold nanoparticles on the fiber surface. The surface density ratio was defined as the ratio of total number of nanoparticles on SEM images multiplied by the mean diameter to the whole area of SEM image. Figure 7 shows that peak resonance (λmax) is a linear function of calculated surface density ratio from the images shown in Figure 6. However, this analysis is unlikely to shed light on the origin of these shifts. Thus it is required to get the deeper insight into the interaction mechanism for quantitative analysis, and based on this, a methodology can be developed to explain the observed phenomenon. In our previous study we have analyzed the red shift of the absorption spectrum using single particle approximation in the framework of Mie’s theory. We had shown that, to describe the gradual red shift, even for the
Figure 5. Absorption spectra of AgNPs for different optical fiber sensor probes with optical density of 2.6 (curve i), 2.3 (curve ii), 2.0 (curve iii), 1.65 (curve iv), 1.2 (curve v), and 0.67 (curve vi). The inset shows the variation of peak (λmax) of absorption spectra with respect to optical density.
To obtain the distribution of immobilized nanoparticles at each stage, we have taken the FE-SEM images of the surface of these probes at the end of the experiments as shown in Figure 6. It is clear from these images that the nanoparticles are inhomogeneously distributed and no aggregates are observed. As expected, the number of nanoparticles increases when the optical density increases. Thus the observed red shift arises
Figure 6. FE-SEM images of AgNP immobilized fiber surface of (a) probe a, (b) probe b, (c) probe c, (d) probe d, (e) probe e, and (f) probe f. 17170
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In DDA method, the peak resonance of the calculated extinction spectrum shifts toward the blue side when the number of dipoles constructing a single nanoparticle increases. In our case, the convergence is achieved when the number of dipoles for the sphere is around 8000 with a diameter of 68 nm as shown in Supporting Information (Figure 2S). Since the observed diameter of the nanoparticle is in the range between 60 to 70 nm with absorption maximum at 425 nm in solution, the extinction spectrum obtained from DDA calculation in Figure 9a, curve i, having 8217 dipoles with diameter 68 nm and resonance maximum at 425 nm is adequate to explain the experimentally observed spectrum of silver nanoparticles in solution. For the Ag particle, the dielectric constant of bulk silver is taken from Palik.36 The construction of two nanoparticles of radius R = 34 nm placed at a distance (center to center) of d nm containing N = 8217 dipoles in each sphere is shown in Figure 9d. To calculate the extinction spectrum of this two-particle system, the angle of incidence of light is kept at the zero degree, and the direction of the propagation is taken along the X-axis. The Y-axis is the direction of the polarization of light parallel to interparticle axis, whereas the Z-axis is perpendicular to that. For Y polarization, when the interparticle distance d = 155 nm, a small red shift (5 nm) of the extinction peak is observed with respect to single nanoparticle (curve ii in Figure 9b). When the nanospheres are getting closer (d = 85 nm, curve iii in Figure 9b), the extinction spectrum becomes broader, and the peak shift is 45 nm. At d = 68 nm, that is, when the nanoparticles touch each other, the band splits into two welldefined and spectrally separated peaks; one is at 433.3 nm and the other one is at 583.8 nm. This phenomenon is the result of strong plasmon coupling and indicates that the electromagnetic interaction between the nanospheres is much more significant when the interparticle separation is 68 nm (formation of the cluster). On the other hand, for the perpendicular polarization (Z direction), a blue shift is observed as shown in Figure 9c. In our experiments, the evanescent fields generated by coupling the xenon white light into the multimode optical fiber were utilized to excite the particle plasmons. The boundary condition satisfied by the evanescent field on fiber surface is continuity of the tangential component of the electric field. Therefore, if the propagation of incident wave is taken in the X direction, then the tangential component is along the Y direction and is parallel to the optical fiber surface. In our experimental observation (Figure 4a) the resonance peak was shifted toward the red side when the nanoparticles were attached on the fiber surface. This trend is quite similar to the shift of the λmax calculated by DDA method in Y polarization. Thus this evanescent wave technique acquires absorption in Y polarization only. The shift of the resonance peak (Δλ) in Y polarization for two-particle system with respect to the single particle at different interparticle distance is given at Supporting Information (Figure 1S). To analyze the effect of distribution of pairs on spectral shift, the Qext spectrum (nmedium = 1.33) calculated from DDA calculations for particular interparticle distance is multiplied by its corresponding observed percentage distribution [C%(di)] of nanoparticle pairs (shown in Figure 8). This procedure provides the weighted contribution of a given distance pairs to the collective spectrum. As an example of this methodology, Figure 10a shows such a weighted Qext spectrum for various observed pairs in the distribution for the probe with optical density 2.6. In this figure, it is observed that the contribution of
Figure 7. Experimentally observed λmax with respect to surface density ratio (%). The straight line represents the linear fit of the data.
spherical nanoparticles the aspect ratio (g) [eq 1 in ref 24] was required to change from 2.0 to 2.57. This was attributed to the departure from the spherical symmetry of the electric field surrounding the nanoparticles. This departure essentially stems from the plasmonic coupling between the nanoparticles. To study further insight into this interaction phenomenon, here we have incorporated two-particle interaction mechanism using DDA theoretical framework. In this respect, we assume that the nanoparticles form pairs only with its closest particle. The collective response is thus the result of the contributions from different pairs distributed on the fiber surface. The numbers of nanoparticle pairs are calculated from the SEM images shown in Figure 6. The percentage distribution with respect to the interparticle distance of these nanoparticle pairs are calculated as, percentage distribution: C %(di) =
ni(drange) ∑i ni(drange)
× 100% (1)
where ni(drange) is the number of nearest neighbor nanoparticle pairs for a particular interparticle distance range as given in the Supporting Information (Table 1S), while the denominator gives the total number of nearest neighbor particle pairs in the SEM image. The percentage distributions of nanoparticle pairs for these six probes are presented in Figure 8a−f. It can be seen from these figures that, as the optical density increases, the number of pairs with interparticle distance below 225 nm increases. Figure 8f shows that the nanoparticle pairs within interparticle distance of 225 nm are very much less compared to the pairs beyond 225 nm, the distance at which the interaction is negligible. Consequently, the collective resonance behaves like single particle response. Therefore, the interaction becomes prominent for higher optical density which causes the spectral shift and broadening of the spectrum. To collate the absorption spectrum with two-particle interaction mechanism, the plasmon coupling effect of collective LSPR is derived within the theoretical framework of discrete dipole approximation using DDSCAT 7.1 developed by Draine and Flatau.32−34 In this computational method32,35 the absorption, scattering, and extinction cross sections of arbitrarily structured target can be calculated. 17171
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Figure 8. Percentage distributions [C%(di)] of nanoparticle pairs from the SEM images at different interparticle distances for optical density of (a) probe a, (b) probe b, (c) probe c, (d) probe d, (e) probe e, and (f) probe f.
(Figure 8f), hence the placement of the particle on the fiber surface is far from each other, and the resultant spectrum is behaving like a single particle response. However in our experiment we have observed that the peak is shifted to 432 nm. Lazarides et al.35 have shown the extinction spectrum of silver truncated tetrahedron as a function of wavelength by DDA method for particles with and without substrate. They have found the significant red shift in the spectrum due to the presence of the substrate. In our approach, if we consider that 432 nm as the plasmon resonance when it binds on the fiber surface which is shifted from solution (425 nm) due to the substrate effect, then the observed shifts due to the plasmonic interaction for OD of 1.2, 1.65, 2.0, 2.3, and 2.6 are 2, 4, 6, 9, and 14 nm, respectively. In Figure 11, the experimentally observed shifts as well as calculated shifts are presented. It can be seen that these shifts are in excellent agreement with the experimental observed shift. Thus, the monotonous shift due to
pairs with separation more than 225 nm is less in OD 2.6 than those for other optical densities (as shown in the Supporting Information, Figure 3S). The summation of all of these weighted contributions provides the resultant collective resonance response which is given as. total Q ext (λ ) =
∑ C%(di) × Q ext(λ , di) di
(2)
where C%(di) is the percentage distribution of pair for interparticle distance di. Qext(λ,di), is the calculated Qext spectrum at distance di by using DDA. In our calculation di = 75, 85, 95, ..., 225. Figure 10b, curve i−vi, shows the resultant collective resonance response of randomly distributed nanoparticles for probe a, probe b, probe c, probe d, probe e, and probe f, respectively. Since the percentage distributions at interparticle distance 225 nm for optical density of 0.67 (probe f) is 80% 17172
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Figure 10. (a) Multiplied extinction spectra at different interparticle distance with percentage distribution for probe a. (b) Resultant collective resonance response for probe a (curve i), probe b (curve ii), probe c (curve iii), probe d (curve iv), probe e (curve v) and probe f (curve vi).
Figure 9. (a) Calculated extinction spectrum of single particle having number of dipoles 8217 and diameter 68 nm (curve i). Calculated Y polarized extinction spectrum of two particles placed at a distance of 155 nm (curve ii), 85 nm (curve iii), and 68 nm (curve iv). Calculated Z polarized extinction spectrum of two particles placed at a distance of 155 nm (curve v) and 85 nm (curve vi). (d) Construction of two silver nanoparticles of radius 34 nm placed at a distance d nm (center to center). (All calculations were carried out with refractive index of medium (nmedium = 1.33.) Figure 11. Comparison of DDA calculated and experimentally observed resonant wavelength shift with respect to optical density.
immobilization of nanoparticles is predominantly governed by the plasmonic coupling between them. To correlate the peak intensities of the absorption spectra, we have multiplied the number of nanoparticle pairs with Qext spectrum of corresponding interparticle distance.
total Q ext (λ ) =
∑ ni(di)×Q ext(λ , di) di
(3)
where ni (di) is the number of nanoparticle pairs at di. 17173
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Figure 12a represents the calculated resultant collective resonance response as given in eq 3 for optical density of 2.6
Figure 13. Comparison of experimentally observed fwhm (full width half maxima) of the absorption spectra and DDA calculated fwhm of Qtotal ext (λ) as a function of optical density.
Thus, using a simple two-particle interaction mechanism, we can explain the spectrum of randomly distributed nanoparticles only by analyzing the microdimensional picture of SEM images. In this methodology, if percentage distributions (C%(di)] are taken as parameters to fit any given spectrum, the distributions of pairs can be extracted from the spectrum of the sensor probe. Since the refractive index sensitivity of Qext spectra depends on the interparticle distance21 of nanoparticle pairs, the randomly distributed nanoparticles pairs on the fiber surface having different interparticle distances would give different refractive index sensitivity. Therefore, the resultant Qext for a particular refractive index of the surrounding medium can be calculated by, Figure 12. (a) Calculated resultant collective resonance response (according to eq 3) at optical density of 2.6 (curve i), 2.3 (curve ii), 2.0 (curve iii), 1.65 (curve iv), 1.2 (curve v), and 0.67 (curve vi). (b) Calculated ln(Qext)λmax by DDA method as a function of different optical densities. A straight line represents the linear fit of the data.
total Q ext (λ , nmedium) =
∑ C%(di) × Q ext(λ , nmedium , di) di
(4)
Thus, using eq 4, the refractive index sensitivity can be predicted from the simulated extinction spectra of different refractive index for a particular randomly immobilized sensor probe. This methodology can be utilized for the development of nanoparticle based optical sensor devices for commercial applications.
(curve i), 2.3 (curve ii), 2.0 (curve iii), 1.65 (curve iv), 1.2 (curve v), and 0.67 (curve vi), respectively. It is observed that ln(Qext)λmax varies linearly with absorbance (optical density) as shown in Figure 12b. Figure 13 shows the variation of the spectral broadening (full width at half-maximum) for the observed spectra and calculated resultant collective resonance spectra. There are two kinds of broadening mechanism those are contributing in the observed spectra. First, the inherent broadening may occur due to different size of nanoparticles present on the fiber surface. Second, the broadening appears due to the plasmon coupling between the randomly distributed nanoparticles. As seen in Figure 13, the trend of the broadening larger than optical density of 1.65 matches with that of the experimentally observed values. However, the difference between the broadening at lower optical density arises because in our analysis we have considered only the plasmon coupling broadening. This departure could be due to fact that, when the particle density is low, the inherent broadening determines the spectral width. But for higher particle density, since the plasmonic effect is dominant, this governs the spectral broadening.
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CONCLUSIONS A systematic study of the absorption spectra of AgNPs during immobilization on the functionalized fiber sensor probe using evanescent wave absorption technique was carried out to establish a relation between particle distribution and their collective localized surface plasmon resonance. The observed red shift of the absorption spectrum with the increment of particle density was attributed to the plasmonic coupling between the distributed nanoparticles. Since the distribution is inhomogeneous, the prediction of the collective response is not very obvious. In this study, the distribution of pairs in terms of interparticle distance obtained from the microdimensional images of randomly distributed nanoparticles are exploited to calculate the collective resultant plasmon resonance using discrete dipole approximation framework. It was found that, using a two-particle interaction mechanism, the shifts of the resultant extinction spectra for the polarization of light parallel to the particle axis were in excellent agreement with the 17174
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observed shifts. This analysis shows that the shift of the spectrum depends on the distribution of the particles rather than the intensity of the spectrum. It also shows that, for the particle density where the interaction between the nanoparticles is significant, the spectral broadening governs by the plasmonic coupling effect. This study provides a quantitative methodology to describe the distributed nanoparticles on the sensor surface when the immobilization is random. Since the refractive index sensitivity depends on the interaction between the nanoparticles, using this methodology the refractive index sensitivity for randomly distributed nanoparticles can be determined from the contribution of individual percentage distribution of pairs. Thus this study essentially provides a guideline for optimizing the sensitivity and wavelength for the designing of this class of optical sensor for large-scale commercial applications.
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ASSOCIATED CONTENT
* Supporting Information S
Peak resonance shift at different interparticle distances for twoparticle system with respect to single nanoparticle (λmax = 425 nm) (Figure 1S). Interparticle distances range on the SEM images for calculating ni(drange) and the interparticle distances taken in the DDA calculation di (Table 1S). Effect of number of dipoles per nanoparticle on the extinction spectrum of single spherical silver nanoparticle (Figure 2S) and the multiplied Qext obtained by DDA calculation with experimentally obtained percentage distribution in different interparticle distance at optical density of (b) 2.3, (c) 2.0, (d) 1.65, and (e) 1.2 (Figure 3S). 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]. Telephone number: (+91-22) 2576 7583. Fax number: (+91-22) 2576 7552. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank to Sophisticated Analytical Instrument Facility (SAIF) of IIT Bombay for providing the FE-SEM facility.
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REFERENCES
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