Article pubs.acs.org/JPCC
Plasmonic Spectroscopy: The Electromagnetic Field Strength and its Distribution Determine the Sensitivity Factor of Face-to-Face Ag Nanocube Dimers in Solution and on a Substrate Nasrin Hooshmand,†,‡ Justin A. Bordley,† and Mostafa A. El-Sayed*,†,|| †
Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States Department of Chemistry, Marvdasht Branch, Islamic Azad University, Marvdasht 72711, Iran || Department of Chemistry, King Abdulaziz University, Jeddah 21589, Saudi Arabia ‡
S Supporting Information *
ABSTRACT: Using the DDA method, the spectral sensitivity of a 42 nm Ag nanocube dimer oriented face-to-face in solution and placed on a substrate was investigated. The sensitivity factor was calculated as a function of both the plasmonic band that was analyzed and the refractive index of the substrate. We found that the maximum value of the electromagnetic field intensity of a given plasmonic band is not directly proportional to its extinction intensity. Also, the sensitivity factor of a plasmonic band does not depend on its extinction intensity, but rather, it is a function of the maximum value of the plasmonic electromagnetic field intensity distribution. The presence of a high refractive index substrate drastically affects the extinction intensity of a given band and selectively enhances specific plasmonic bands on the basis of their electromagnetic field distribution. The distribution of the electromagnetic field intensity on the surface of the Ag nanocube dimer is also affected by the presence of a substrate with a high refractive index. As the refractive index of the substrate increases, the substrate serves to reduce the maximum value of the plasmonic field intensity. Consequently, and as is known, the sensitivity factor decrease as the refractive index of the substrate increases. This suggests that when designing a good sensor, it is imperative to use a substrate with a dielectric function smaller than that of the solutions being detected.
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INTRODUCTION
The above sensitivity factor of a nanoparticle is strongly dependent on the plasmonic nanoparticle shape. Shapes having sharp corners have been shown to be most promising for nanoparticle sensing applications.18,19 Sharp corners facilitate the development of a high density of similarly oriented oscillating dipoles during their coherent resonant oscillation. This leads to the following (1) high electromagnetic field and intraoscillating dipole repulsions; and thus (2) large stabilization energies per unit change in the medium dielectric function (i.e., large values of sensitivity factors). Along with the enhanced sensitivity, these shapes also exhibit drastically enhanced electromagnetic fields. In the present publication, we show the unique relationship between the magnitude of the electromagnetic field in a plasmonically coupled system of two silver nanocubes at 2 nm separation and the values of their corresponding sensitivity factors. Within the last 5 years, studies of the optical properties of two coupled nanoparticles in close proximity to each other have led to a new development in the field of nanoparticle sensing.20−22 As two nanoparticles are brought in close proximity to each other, a coupling between the resonant
The local surface plasmon resonance (LSPR) properties of plasmonic nanoparticles in close proximity to each other are strongly dependent on the size, the shape, the interparticle separation, as well as the dielectric function of the surrounding medium and the supporting material (substrate).1−9 These properties make the nanoparticles useful in a variety of important applications such as imaging, plasmonic devices,10 near field scanning optical microscopy, optical energy transport, and chemical and biological sensing.11−14 In most sensing applications, the sensitivity of the LSPR to either the surrounding medium or the interparticle separation is exploited for enhanced molecular detection. In order to predict the efficacy of a specific plasmonic nanoparticle system for sensing applications, a specific figure of merit was developed, the sensitivity factor (SF).15,16 As the refractive index of the surrounding medium increases, there is a reduction in the repulsion between the in-phase oscillating dipoles of a given plasmonic band. This reduction decreases the energy of that oscillator, thus resulting in a red shift of its plasmonic band. As a result, the sensitivity of a plasmonic band, and the SF, is then related to the magnitude of the observed shift of the plasmonic band maximum per unit change of the refractive index of the surrounding medium.17 © XXXX American Chemical Society
Received: June 5, 2015 Revised: June 18, 2015
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DOI: 10.1021/acs.jpcc.5b05395 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C
to the external field and their nearest oscillating dipole neighbors is solved self-consistently using Maxwell’s equations. The size of the cube is defined by an equal volume of a sphere with an effective radius reff = (3v/4π)1/3. Here the reff for that of the pair of the cube by itself is 32.82 nm and that of the dimer and substrate is 37 nm. Water, ethanol, carbon tetrachloride, and toluene are used as the medium surrounding the dimer with a refractive index (RI) ranging from 1.33 for water to 1.495 for toluene. It was found that increasing the length, width, or the thickness of the substrate did not alter the results.28 The refractive index of silver cubes is assumed to be the same as that of the bulk metal, and the refractive index of the glass and AlGaSb were 1.46 and 4.3, respectively. The plasmonic electromagnetic field intensity (in log scale of |E|2/| E0|2) generated at various wavelengths of excitation was determined for the top surface of the dimer, unless otherwise noted.
electronic oscillations of each nanoparticle results in a drastic increase in the electromagnetic field that is generated. This near field coupling behavior of a nanoparticle dimer was previously described by a near exponential decay behavior, commonly known as the plasmon ruler equation.23 However, this dipolar coupling dependence fails at the short separations distances. The coupling behavior of a nanoparticle dimer at ∼2−10 nm separations has been further explored, and it has been found that the nonlocal optical properties of oscillating electrons, gap morphologies, and the distribution of the electromagnetic field that is generated for a specific plasmonic band influence the coupling behavior of a dimer. Furthermore, as the separation distance decreases even further (
