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Sculpting the Analytical Volume in and around Nanoparticle Sensors Using a Multilayer Geometry Anil K. Kodali,†,‡ Matthew Schulmerich,‡,§ Rohun Palekar,§ and Rohit Bhargava*,†,‡,§,∥ †

Department of Mechanical Science and Engineering, ‡Micro and Nanotechnology Laboratory, §Department of Bioengineering, University of Illinois Cancer Center and Electrical and Computer Engineering, and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ∥

ABSTRACT: The use of structured nanoparticles as optical contrast agents has led to new sensing opportunities in localizing the analytical volume within or outside the particle. Here we examine the use of structured nanoparticles for controlling the sensed analytical volume and figures of merit for their use. Nanolayered alternating metal− dielectric particles (nanoLAMPs), consisting of metal−dielectric nanospheres, are a flexible and highly tunable structure and used here to illustrate the concept of sculpting the analytical volume associated with a nanoparticle. The alternating metal and dielectric shells in LAMPs are designed such that, when illuminated, the plasmonic coupling of metal shells results in amplified electric fields in specific volumes. The strength and extent of regions with amplified fields (hot spots) in and around a LAMP are at the expense of other regions with depleted fields. A rigorous Mie theory formulation is used to model electric field redistributions. A genetic algorithm-based strategy is then employed to design LAMPs that selectively enhance the response of analyte molecules located either outside or in various dielectric layers through electric field redistribution. We demonstrate that it is possible to localize the analytical volume to within or outside the particle quite efficiently. Further, the analytical figures of merit (localization and amplification of signal as well as contrast between sensed species and background) are optimized and limits to the same are described. The strategy proposed here is a general route to engineer a palette of probes with highly specific detection capabilities using spectroscopy techniques based on surface-enhanced scattering, absorption, or emission processes.

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energy loss not used for sensing. In most implementations, however, signal enhancements both within the particle and in the environment are achieved. This leads to a decrease in the selectivity of the signal and reduces the analytical fidelity of the recorded data. Control over the analytical volume, hence, directly determines the effectiveness of the nanoparticle as a sensor. Here, we show that the analytical volume of nanoparticle probes can be effectively controlled using a nanoLAMP17 geometry. We sought to examine theoretically the use of this template by examining three important facets amplification of signal from the desired analytical volume, maximizing the contrast between the desired analytical signal and the background arising from outside the designed volume, and finally, the optimality of amplification and contrast relative to each other. NanoLAMPs are multilayered nanospheres with alternating metal and reporter-embedded dielectric layers as shown in Figure 1. To distinguish between sensing of molecules inside and outside the particle, we term the sensed species reporters and analytes, respectively. While reporters are typically embedded prior to use of nanoparticles, analytes enter the analytical vicinity only after the nanoparticles are deployed for sensing. The spherical symmetry of nanoLAMPS makes them attractive in terms of design simplicity, fabrication, and

llumination of a metal nanoparticle by light induces waves of surface-confined collective electronic oscillations. The consequent redistribution of the space around the particle into enhanced electromagnetic (EM)-field regions (hot spots)1 and depleted EM-field regions2 can be exploited to sense the presence of molecular species around the particle. Due to this capability, nanoparticles have generated tremendous interest for analytical sensing3for example, as direct optical reporters,4 tags for conjugated species,5 or as amplifiers of the analytical signal of the surrounding nanoenvironment.6 An exponential decay in electric field that depends on the composition and size of the particle7 provides a characteristic sensing volume around the particle.8 The strength, extent, and the wavelength dependence of this modified electric field are also affected by proximity and orientation of other metallic particles9,10 or surfaces. As opposed to solid particles, nanostructured particles such as nanoshells,11 particles containing controlled colloids,12 nanocrescents,13 nanoscale layered alternating metal−dielectric particles (nanoLAMPs),14 shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINER),15 and composite organic− inorganic nanoparticle (COIN)16 geometries have recently been studied as sensors. While some structures enhance the signal of molecular species within the particle, others are designed to probe the environment outside the particle. In the first class of particles, the ideal structure should enhance the properties within the particle but not its environment. For the latter class, the enhancement is ideally concentrated in the environment and minimized within the particle to minimize © 2013 American Chemical Society

Received: September 21, 2012 Accepted: February 11, 2013 Published: February 28, 2013 3842

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Figure 1. View of half of odd-layered/dielectric core (A) and even-layered/metallic core (B) spherical LAMP structures. (C) A 2D sectional view of L-layered LAMP structure with parameters that are of significance in modeling, radii (r) and refractive index (m) of different layers.

ment or quenching factors (G) can thus be evaluated as a volume integral of square or fourth power of local E-fields.

application. Nanoshells, SHINERS, and multilayered nanoshells18 (MNS) can be considered as subclasses in the generalized nanoLAMP framework. While elegant analytical solutions and fabrication approaches to nanoshells and MNS exist,19−21 generalization to the nanoLAMP geometry can greatly increase sensitivity and multiplexing capabilities by expanding the number of design parameters. Genetic algorithms (GA)-based optimization, for example,22 can be used to optimize structures for applications. A GA-based23 approach in designing a palette of Raman14 and optical17 reporters with optimal sensitivity has also been reported for nanoLAMPs. Here, we report the ability to design the selectivity of both reporter and analyte signals by controlling the spatial distribution of electromagnetic fields. Through a GA-based design optimization, we show that structures can be created with designer sensitivity for organic reporters embedded in any chosen dielectric layer while maintaining a specific contrast ratio for the signal with respect to the particle environment and other dielectric layers. Similarly, we also describe utilizing LAMPS to enhance or control the contrast of the analytical signal from its background.

G L = G F = GA = G =

∭ |E loc(ωo)|2 cr dV

(1a)

or GR =

∭ |E loc(ωo)|4 cr dV

(1b)

Several considerations are important regarding the sensed molecular species. The concentration of molecules in the volume of interest (V) is incorporated into eq 1 by using a loading factor of uniform concentration per unit volume cr. We assume a low loading of cr = 1% for the studies here. Though quantification of reporter loading has been reported to be approximately 10-fold higher,31 the lower concentration used here is a compromise between typical reporter loading and low level of analyte signal. As the concentration is a simple scaling factor, further, the assumed loading does not detract from the generality of the results. Since the general case is considered here, the molecules are assumed to be uniformly dispersed in the analytical volume rather than being attached, for example, as a surface-assembled monolayer (SAM).32 The distribution of the local field (Eloc) is key to predicting sensors’ responses for all optical techniques. We have earlier adapted a recursive numerical implementation33 of an analytical solution based on layered-Mie theory34 for fast and accurate evaluations for millions of LAMPs that provides feasible inputs to algorithms for optimal solutions. Although the analytical solution is well-known, our implementation involves stable and fast numerical calculations in general as described in earlier publications.17 By using appropriate cutoff for the maximum order of vector spherical harmonics (VSH)35 and stable recursive evaluations30 of logarithmic derivative and ratio functions involved, an accurate mathematical solution can be obtained for coefficients and fields in each layer. For metal layers of thickness greater than 10 nm, it is typically acceptable to use the values obtained from bulk dielectric constants reported in literature.36 In case of shells thinner than 10 nm, we modify the imaginary part of bulk dielectric constant to account for restricted mean free path according to the previously reported methods.37 The integrals in the spherical shells are

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THEORY AND METHODS The nanoLAMP template can potentially be used in designing labels and/or as signal enhancing particles for different spectroscopic techniques based on luminescence,24 fluorescence,25 absorption,26 and scattering27 processes. Electromagnetic effects typically are a dominant contributor to the signal attained in all these techniques;28 hence, we choose here to design the electromagnetic enhancement ignoring other effects. In particular, embedding the reporter in the dielectric shells shields them from chemical effects of interactions with the metal layers while the protective dielectric layer29 shields the analyte from metal interaction by eliminating contact with the outermost metal shell. For surface-enhanced luminescence, fluorescence, or absorption the electric field-induced change for a molecule located in the analytical volume scales as the square of local field, whereas for surface-enhanced Raman scattering (SERS)30 the enhancement achieved scales as the fourth power. The net enhance3843

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evaluated using a standard numerical approach.38 The details of the GA-based approach for optimization of enhancements are discussed earlier.17 The constraints on the thickness are imposed according to the recent experimental implementations of such geometries.39−41 A minimal thickness constraint of 1 nm is imposed for the silica layers, and a minimal thickness constraint of 2 nm is imposed for the metal layers according to the current fabrication limits.42,43 Similarly a size constraint of 10 nm is imposed for metal and silica cores. These values reflect commonly encountered limits of fabrication.

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RESULTS AND DISCUSSION Surface plasmon resonances associated with each metal shell and the coupling can be theoretically examined to choose appropriate layer sizes for desired resonances in simple structures.10,44 The nonlinearity of the problem, however, rapidly complicates analysis with multiple resonances and their additions being involved in the final response of structures with a larger number of layers. Hence, we explicitly design and optimize the E-field distribution and spatially confine the enhanced E-fields to a particular region in the vicinity of LAMPs using numerical solutions. The large number of parameters imparts both flexibility in the design of responses and constrains predictions to be made only for specific conditions or structures. The effects of variability with small changes in parameters have been studied in depth elsewhere;45 while specific values and optimal designs may change somewhat with the choice of materials and the values of parameters, specific choices serve to illustrate the generality of the design approach presented here. While predictions are specific, global trends can still be deduced by examining a set of values as a function of, for example, size, composition, or excitation wavelength. Sculpting Fields within and around LAMPs. Figure 2 demonstrates the ability to localize the E-field, enhancement factor (G), and hence, the sensitivity to reporters in different dielectric layers in five- and six-layered silver−silica nanoLAMPs of fixed size (200 nm) and specific excitation (785 nm). The structures shown are optimized such that the ratio of total enhancement for the reporter in a desired layer to that in other layers is maximized under the constraint of keeping the total size constant. For the five-layered LAMPs, the structure that maximizes the E-field to the silica layer between the first and second silver layers (Figure 2B) possesses the largest G as illustrated by the E-field distribution in the xy-plane. This structure has comparatively thicker metal shells as that efficiently couples the electric field to the desired location as well as reduces the volume of reporter available in the dielectric shells. By increasing the dielectric core size and/or by minimizing the thicknesses of metal layers, for example, it is possible to tune the largest G values to within the silica core (Figure 2A) or to the outermost silica layer (Figure 2C). Relatively similar structures, hence, can be tuned to provide spatially varied hot spots simply by adjusting the structure of the nanoparticle, as indicated by tuning the hot spots in the other layers of the nanoLAMPs in Figure 2. Similar results can be observed for six-layered silver−silica LAMPs. When a larger silver core is chosen for the structure, the largest G is attained in the silica layer surrounding the core (Figure 2D). The optimal structures to maximize G values in the outer silica layers (Figure 2, parts E and F) possess a smaller core and thicker outer metal shells, as may be expected. The localization of the hot spots comes at a cost, however. The

Figure 2. Optimization of local sensing capability by localizing the hot spots internally to innermost (A and D), first outer (B and E), and outermost (C and F) silica layers illustrated by plotting E-field distributions in the xy-plane for five-layered (A−C) and six-layered (D−F) silver−silica LAMPs. The illumination wavelength is 785 nm, and the geometrical boundaries are depicted using black dotted lines. The radii for the optimal structures designed are (A) 58, 62, 94, 99, and 100 nm, (B) 5, 32, 39, 67, and 100 nm, (C) 5, 7, 46, 56, and 100 nm, (D) 23, 27, 51, 72, 83, and 100 nm, (E) 5, 10, 39, 49, 81, and 100 nm, and (F) 5, 47, 49, 50, 60, and 100 nm. (G) Internal E-field distribution in LAMPs in panels A−F along the xy-plane and geometrical depiction.

absolute values of the maximum fields attained for these structures are lower compared to what would be attained in the silica layer surrounding the silver core. In terms of overall signal from the particle, the situation is somewhat mitigated by the larger volume attained over the same radial distance as we are farther away from the core. Hence, a particular experiment may utilize the inner or outer core amplification for a given size and structure of the particle depending on the particular conditions. The flexibility in tuning the position and strength of the EM localization as well as the interplay with the analytical test for which the particles are to be used represents an unprecedented opportunity to tailor and optimize the use of nanoparticles as probes. Just as for reporters within the LAMPs, the same structures can also be designed to enhance the E-field and the response of analyte molecules in their environment. For the purposes of calculation, we consider a spherical analytical volume with the LAMP in the center. Ten times the probe size is chosen to surely encompass the entire analytical volume that can be affected by a LAMP as the EM fields decay exponentially away from its surface. Figure 3A shows the electric field intensities along the x-axis for optimal 100 nm sized LAMPs of different layers at 785 nm excitation. Compared to a bare gold sphere, the attained enhancement can be much higher for LAMPs. As the number of layers increase, the ability to extend the associated hot spot further into the LAMP environment increases. As seen for the optimal Raman LAMPs with reporters,13 the hot spots attained with optimal four-layered LAMP and six-layered LAMP are equally strong as are the hot spots attained with optimal five-layered and seven-layered 3844

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likely arises from the formation of a “cold spot” due to the multipole interaction of the individual metal layers. The depletion of the field suggests an alternative sensing strategy in which the signal of the analyte is “bleached” in the sense of fluorescence photobleaching or spectral hole burning. While the mechanisms of the two phenomena are entirely distinct from the purely electromagnetic depletion here, the net effect is that the signal of an analyte will be decreased and can become insignificant. As opposed to fluorescent photobleaching, however, there is no change in the sensed molecule, and its signal can be easily recovered as it exits the sensing volume defined by the cold spot. Utilization of the concepts of analytical sculpting can possibly represent an alternative approach to super-resolution sensing around these nanoparticles.46 Simultaneous Depletion and Enhancement. Considering the signal depletion further, the nanoLAMP framework can be used to design structures with optimized depletion capabilities as demonstrated for signal enhancement. A general strategy to design such structures is to use thicker outer metal layers and optimize the overall particle for the smallest possible electric fields within the structure. To demonstrate the generality of this approach, we designed five-layered copper− silica LAMPs for maximizing or minimizing the enhancement factor of contained reporter molecules for an excitation of 633 nm. Figure 4 illustrates the hot spots and cold spots attained in the particle interior by plotting E-field distribution in the xyplane. In both cases, the fields in the interior dielectric layers are enhanced or decreased up to 3 orders of magnitude compared to the exterior, extending the capability to create a palette of same-sized probes with a designed sensitivity and large dynamic range. Attaining high and low enhancements, the ability to adjust the analytical distance around the particle, and extending the dynamic range using the same particle size are obviously benefits that cannot be attained using bare nanoparticles or simple structures. Another important facet of employing structured particles with analytical sculpting is the ability to use materials that have not been previously utilized for sensing. For example, silver−silica structures are common due to the large enhancements they offer in simple geometries and due to the spectral location of their primary resonance peak(s) (Figure 5). Similarly, gold−silica structures are very effective

Figure 3. Optimization of local sensing capability by localizing a hot spot to the exterior of 100 nm sized gold−silica LAMP structures. Efield distributions in the xy-plane, for structures with two to seven (C− H) layers compared to a bare gold sphere (B) at 785 nm excitation. The electric field intensity along the x-axis with distance from the surface of these LAMPs is depicted in panel A. The radii of layers in the optimal structures derived are (B) 50 nm, (C) 27 and 50 nm, (D) 19, 35, and 50 nm, (E) 25, 38, 48, and 50 nm, (F) 7, 9, 10, 49, and 50 nm, (G) 5, 9, 25, 38, 48, and 50 nm, and (H) 16, 18, 19, 21, 32, 44, and 50 nm. The internal field distributions are deemed insignificant in the evaluations here, and the LAMP structures are shown in white for clarity in visualizing field distributions.

LAMPs. First, it must be noted that the odd-layered (dielectric core) structures provide a weaker intensity of the electric field. Second, as may be expected, there is an upper bound to the sensing volume around the particle, as was reported previously for inside the particle. The total enhancement of molecular signal, however, depends on the combined effect of the enhanced electric field and the volume over which it is distributed. Hence, direct comparisons of the enhancement capability inside and outside the LAMP are difficult. From these results, for a 785 nm illumination and 100 nm LAMP size, it appears that a LAMP with four layers provides as much an enhancement as would be possible for this size. Other application-specific observations can similarly be made using such design principles. Third, an interesting behavior is seen for four-layered and six-layered structures chosen. We notice a dip in the intensity between 100 and 500 nm in Figure 3A. This

Figure 4. E-field distributions in the xy-plane for five-layered copper−silica LAMP structures, optimized to demonstrate depletion (A) and enhancing (B) capabilities for reporter molecules contained within the particle at an illumination wavelength of 633 nm. The geometrical boundaries of different layers are depicted with black dotted circles, and the radii of the optimal LAMPs designed are (A) 5, 7, 8, 98, and 100 nm and (B) 5, 16, 23, 51, and 100 nm. (C) Internal E-field distribution along the xy-plane for LAMPs (A and B) and their geometrical depiction. 3845

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Figure 5. E-field distribution in the xy-plane for a single four-layered silver−silica LAMP with an enhanced sensing capability in the interior at 532 nm excitation (A) and quenched sensing capability at 1064 nm illumination (B). The radii of the layers in the LAMP designed are 23, 115, 199, and 200 nm. (C) Internal E-field distribution for excitations (A and B) along the xy-plane and geometrical depiction for this LAMP.

specificity can be quantified by using a contrast ratio which we define as

and preferable in biological detection purposes due to the inert nature of gold. As a consequence, copper−silica structures have not been thoroughly examined to date. The results here establish an example of our ability to design ability utilizing copper−silica LAMPs. In general, it may be possible to access high enhancements, tunability of the sensitivity, and sensing volume as well location of plasmonic peaks using materials that are not commonly used for nanoparticle sensing. Less costly and new routes to fabrication may indeed become possible with the use of new materials that were previously limited, while additional properties such as magnetic response can be incorporated without a compromise in the optical sensing capability by structuring the nanoparticle. In addition to the flexibility in use of materials, control of sensing volumes at multiple illumination wavelengths is also possible in our approach. The multiple excitation capability of LAMPs has been discussed earlier, in which we observed that a flat spectral response can be achieved to use the same particle effectively at different wavelengths. Here, we illustrate the ability to design a single structure that can act both as an amplifier and depleter of the reporter response at different wavelengths. The application of this concept will enable an extension of the dynamic range of the sensing particle. To illustrate the concept, we enhance the within-particle reporter signal at 532 nm illumination while depleting the interior reporter signal at 785 nm illumination, two wavelengths commonly used for excitation in SERS. Multimodal detection, where the same structure can be used to detect the presence of highly abundant species (depleted at the excitation frequency) and low concentration (enhanced at the frequency excitation), will be enabled by this design strategy simply by employing two wavelengths. Between the two excitations here, for example, a dynamic sensing range of over 12 orders of magnitude is attainable. The ease of designing multiple excitation capabilities is typically higher for particles of larger sizes. A larger size of 400 nm is chosen here. If the application constrains the nanoparticle size, an optimization can be carried out to determine the performance of the optimal enhanced−depleted pair for any given size and wavelengths. Sensitivity and Selectivity. The sensitivity of a particular analytical volume can be quantified by the enhancement factor G. Another figure of merit in sensing, however, depends on separating the probe signal from that of its analytical background. We theoretically examine this specificity (selectivity) when nanoLAMPs are used for SERS sensing. The

CR =

G RLAMP G RVicinity

(2)

GLAMP R

where is the Raman enhancement achieved for reporter volume within the particle and GRVicinity is the Raman enhancement attained for the analyte volume in the environment. The relevant vicinity is again defined by a 1 μm sphere with LAMP at its center, as disused previously. Designing labels with optimal sensitivity, while maintaining a particular contrast ratio, is of significance in biological imaging applications for accurate quantification of the tagged molecules. We designed optimal nanoLAMPs of various sizes at 785 nm illumination, a commonly used excitation frequency for biological applications, for this purpose. The goal here was to discover the highest contrast ratios that could be obtained at this excitation for a given set of materials to establish the performance limits of LAMPs for biomedical sensing. Determining the optimal structures globally would allow us to fabricate highly efficient probes, while the knowledge of performance limits (enhancement and contrast ratio) for every size would allow for designing and understanding experiments in which the size of the particle is constrained. Hence, we developed plots for the optimal structures for each size and composition (number of layers) at the wavelength used for a variety of contrast ratios. The genetic algorithm is chosen to pick structures for which contrast ratio is at least the considered value. Figure 6 depicts the optimal enhancement factors achieved for gold−silica nanoLAMPs of different sizes and layers with different contrast ratios. The sizes considered are to be in the range of 30−150 nm, which is relevant for biological sensing purposes. The first conclusion from these results is that the optimal enhancement factor, GR, and contrast ratio, CR, are obviously inter-related. The CR can be considered to be the ratio of the signal of the probe to the “noise” of the analytical background. This is the worst possible case as we assume that the background and reporter have total spectral overlap. Obviously, if there is no spectral overlap, the noise is dominated by measurement noise. Considering enhancement at several CR that may be expected in experiments allows the determining of requisite size and structures for a particular application. As the required CR increases, we note in the second conclusion, some sizes and numbers of layers are unable to meet the criterion for minimum CR. These sizes in the contour plots are depicted in black 3846

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nanostructured particles and the subsequent validation of predictions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The reported work was supported by the Beckman Institute for Advanced Science and Technology by a Seeding New Frontiers Grant and by the National Science Foundation via Grant CHE0957849.

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REFERENCES

(1) Camden, J. P.; Dieringer, J. A.; Wang, Y.; Masiello, D. J.; Marks, L. D.; Schatz, G. C.; Van Duyne, R. P. J. Am. Chem. Soc. 2008, 130, 12616−12617. (2) Mahmoud, M. A.; El-Sayeed, M. A. Nano Lett. 2009, 9, 3025− 3031. (3) Jain, P. K.; Huang, X.; El-Sayed, I. H.; El-Sayed, M. A. Acc. Chem. Res. 2008, 41, 1578−1586. (4) Baciu, C. L.; Becker, J.; Janshoff, A.; Sonnichsen, C. Nano Lett. 2008, 8, 1724−1728. (5) Doering, W. E.; Nie, S. Anal. Chem. 2003, 75, 6171−6176. (6) Kneipp, J.; Kneipp, H.; Kneipp, K. Chem. Soc. Rev. 2008, 37, 1052−1060. (7) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668−667. (8) Haes, A. J.; Zou, S.; Schatz, G. C.; Van Duyne, R. P. J. Phys. Chem. B 2003, 108, 109−116. (9) Jain, P. K.; El-Sayed, M. A. Chem. Phys. Lett. 2010, 487, 153−164. (10) Braun, G. B.; Lee, S. J.; Laurence, T.; Fera, N.; Fabris, L.; Bazan, G. C.; Moskovits, M.; Reich, N. O. J. Chem. Phys. C 2009, 113, 13622−13629. (11) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. Science 2003, 302, 419−422. (12) Wustholz, K. L.; Henry, A.-I; McMohan, M.; Freeman, R. G.; Valley, N.; Piotti, M. E.; Natan, M. J.; Schatz, G. C.; Van Duyne, R. P. J. Am. Chem. Soc. 2010, 132, 10903−10910. (13) Bukasov, R.; Shumkaer-Parry, J. S. Nano Lett. 2007, 7, 1113− 1118. (14) Kodali, A. K.; Llora, X.; Bhargava, R. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 13620−13625. (15) Li, J. F.; Huang, Y. F.; Ding, Y.; Yuang, Z. L.; Li, S. B.; Zhou, X. S.; Fan, F. R.; Zhang, W.; Zhou, Z. Y.; Wu, D. Y.; Ren, B.; Wang, Z. L.; Tian, Z. Q. Nature 2010, 464, 392−395. (16) Su, X.; Zhang, J.; Sun, L.; Koo, T.-W.; Chan, S.; Sundararajan, N.; Yamakawa, M.; Berlin, A. A. Nano Lett. 2005, 5, 49−54. (17) Kodali, A. K.; Schulmerich, M. V.; Palekar, R.; Llora, X.; Bhargava, R. Opt. Express 2010, 18, 23302−23313. (18) Bardhan, R.; Mukerjee, S.; Mirin, N. A.; Levit, S. D.; Nordlander, P.; Halas, N. J. J. Phys. Chem. C 2010, 114, 7378−7383. (19) Xu, H. Phys. Rev. B 2005, 72, 0734051−0734054. (20) Averitt, R. D.; Westcott, S. L.; Halas, N. J. J. Opt. Soc. Am. A 1999, 16, 1824−1832. (21) Hu, Y.; Fleming, R. C.; Drezek, R. A. Opt. Express 2008, 16, 19579−19591. (22) Yelk, J.; Sukharev, M.; Seideman. J. Chem. Phys. 2008, 0647061−064706-7. (23) Deb, K. Multi-Objective Optimization Using Evolutionary Algorithms; John Wiley & Sons: Chichester, U.K., 2001. (24) Kulakovich, O.; Strekal, N.; Yaroshevich, A.; Maskevich, S.; Gaponenko, S.; Nabiev, I.; Woggom, U.; Artemyev, M. Nano Lett. 2002, 1449−1452.

Figure 6. Optimal Raman enhancement factors (GR) attained for gold−silica LAMPs as a function of total particle size while maintaining a given contrast ratio (CR). GR attainable is shown for even-layered (metallic core) LAMPs for CR values 0.1 (A), 1 (C), 10 (E), 100 (G), and 1000 (I). For odd-layered (dielectric core) LAMPs, GR attainable is shown for CR values 0.1 (B), 1 (D), 10 (F), 100 (H), and 1000 (J).

indicating that there is no qualified signal enhancement obtained. As the CR increases, third, a larger size is required. This is a direct consequence of both the need to confine the fields to within the particle physically as well as to structure the numbers of layers such that the inner core is more enhanced. Finally, for even-layered (metallic core) LAMPs, the total size is smaller and the enhancements attained are higher.

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CONCLUSIONS The ability to control the spatial redistribution of electromagnetic fields and, hence, the analytical volume by structuring a nanoparticle is proposed and theoretically analyzed. The structures can be designed such that control over the response of molecules at the interior as well as the exterior of the particle is possible. We show that the controlled amplification or depletion of signal can be sculpted over orders of magnitude and the combined effect of depletion and amplification can be used to extend the dynamic range of a palette of nanoLAMPs. New materials and multiple wavelengths can be employed by careful design, providing new flexibility and potential for multifunctional probes. Theoretical design procedures and approaches are crucial in fully exploiting the optical tunability of LAMPs in sensing applications employing surface-enhanced spectroscopy. We demonstrate that the contrast ratio can act as a figure of merit to achieve analytical sensitivity and selectivity subject to design limits. These theoretical observations signal the potential and need for research into fabrication of 3847

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(25) Zhang, J.; Malicka, J.; Gryczynski, I.; Lakowicz, J. R. J. Phys. Chem. B 2005, 109, 7643−7648. (26) Kundu, J.; Le, F.; Nordlander, P.; Halas, N. J. Chem. Phys. Lett. 2008, 452, 115−119. (27) Moskovits, M. Rev. Mod. Phys. 1985, 57, 738−826. (28) Schatz, G. C.; Van Duyne, R. P. Handbook of Vibrational Spectroscopy; Wiley: New York, 2006. (29) Mulvaney, S. P.; Musick, M. D.; Keating, C. D.; Natan, M. J. Langmuir 2003, 19, 4784−4790. (30) Xu, H.; Wang, X. H.; Perrsson, M. P.; Xu, H. Q.; Kall, M.; Johansson, P. Phys. Rev. Lett. 2004, 93, 243002. (31) Sivapalan, S. T.; Devetter, B. M.; Yang, T. K.; van Dijk, T.; Schulmerich, M. V.; Carney, P. S.; Bhargava, R.; Murphy, C. J. ACS Nano 2013, 7, 2099−2105. (32) Schultz, M.; Kustner, B.; Bauer, M.; Schmuck, C.; Schlucker, S. Small 2010, 6, 733−737. (33) Kodali, A. K.; Bhargava, R. Proc. SPIE 2008, 7032, 7032V. (34) Johnson, B. R. Appl. Opt. 1996, 35, 3286−3296. (35) Wiscombe, W. J. Appl. Opt. 1980, 19, 1505−1509. (36) Palik, E. D. Handbook of Optical Constants of Solida III; Academic: New York, 1998. (37) Khlebtsov, B.; Khlebtsov, N. J. Biomed. Opt. 2006, 044002. (38) Pierce, W. H. Math. Tables Other Aids Comput. 1957, 11, 244− 249. (39) Lim, D. K.; Jeon, K. S.; Hwang, J. H.; Kim, H.; Kwon, S.; Doug Suh, Y.; Nam, J.-M. Nat. Nanotechnol. 2011, 6, 452−460. (40) See, K. H.; Mullins, M. E.; Mills, O. P.; Heiden, P. A. Nanotechnology 2005, 16, 1950−1959. (41) Caruso, F.; Spasova, M.; Salgueirino-Macceira, V.; Liz-Marzan, L. M. Adv. Mater. 2001, 13, 1090−1094. (42) Nomura, K.; Fujii, S.; Ohki, Y.; Awazu, K.; Fujimaki, M.; Tominaga, J.; Fukuda, N.; Hirakawa, T.; Rockstuhl, C. Jpn. J. Appl. Phys. 2008, 47, 8642−8643. (43) Xia, X.; Liu, Y.; Backman, V.; Ameer, G. A. Nanotechnology 2006, 17, 5435−5440. (44) Radloff, C.; Halas, N. J. Nano Lett. 2004, 4, 1323−1327. (45) Kodali, A. K.; Bhargava, R. Theor. Chem. Acc. 2011, 130, 991− 1000. (46) Stranahan, S. M.; Willets, K. A. Nano Lett. 2010, 10, 3777− 3784.

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dx.doi.org/10.1021/ac302744g | Anal. Chem. 2013, 85, 3842−3848