ARTICLE pubs.acs.org/JPCC
Anisotropic Plasmonic Sensing of Individual or Coupled Gold Nanorods Guowei Lu,*,† Lei Hou,† Tianyue Zhang,† Wenqiang Li,† Jie Liu,† Pascal Perriat,‡ and Qihuang Gong*,† † ‡
Department of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, 100871 Beijing, China MATEIS (GEMPPM) - UMR CNRS 5510, INSA de Lyon, B^atiment Blaise Pascal, 7 avenue Jean Capelle, 69621 Villeurbanne Cedex, France
bS Supporting Information ABSTRACT: We perform a theoretical investigation of individual and coupled gold nanorods as plasmonic nanosensors using the finite-difference time-domain method. Key features of single-nanorod sensors are discussed. The sensitivity distribution of an individual nanorod is anisotropic. The characteristic sensitivity decay length of a single-nanorod sensor is comparable to its diameter. Plasmonic sensing abilities are additive, so analyte-detection sensitivity is not affected by substrates or surface treatments; shifts caused by analytes are only determined by their positions relative to the sensor. Coupled nanorods enhance and concentrate plasmonic sensitivities, and the sensitivity within the gap can be over an order of magnitude higher than that at the nanorod cylinder. The sensitivities of coupled nanorods are only higher than those of individual nanorods when the analytes are anchored within the gaps between nanorods. The calculations show that a single biological molecule can be detected by optimizing nanostructure design and surface treatments to anchor analytes locally on high-sensitivity areas of the sensor surface. Our simulation results assist the design and optimization of plasmonic nanosensors, using single or coupled nanorods.
’ INTRODUCTION Localized surface plasmon resonances (LSPRs) of metallic nanostructures, which are associated with collective oscillations of free electrons, can generate a large field confinement in an extremely small volume.13 This unique optical property of plasmonic nanostructures has led to the development of a new class of label-free biomolecular sensors. The light-scattering and absorption properties of noble-metal nanostructures are functions of the local environment.4,5 In LSPR nanosensors, therefore, highly sensitive transduction of binding events at their surface into macroscopically measurable optical signals is possible. The use of this principle allows one to build ultrasmall plasmonic sensors that can detect analytes (e.g., biomolecules) in volumes down to attoliters.69 It has been shown that the sensitivity of a sensor to its environment can be enhanced by tuning the geometry of the plasmonic nanostructure. Nanoprisms, nanorods, and nanoshells have high LSPR sensitivities.1016 Miniaturization of the sensor to the level of a single nanostructure reduces the detection system to a scale that is commensurate with the sizes of biomolecular analytes. Recently, progress has been made in producing LSPR sensors with individual nanostructures. Singlenanostructure sensors offer improved absolute detection limits (the total number of molecules detected) and enable higher spatial resolution in multiplexed assays. In addition, single nanostructures with narrow bandwidths can improve signal-to-noise resolution. They also have promising applications for measurements in aqueous solutions or inside cells and tissues where fixed arrays are unable to penetrate.9,1727 r 2011 American Chemical Society
Although much experimental and theoretical effort has been devoted to designing single gold nanorods as plasmonic nanosensors,21,25,28 understanding of the rational design and optimization of nanorod sensors is still inadequate. For instance, the order of magnitude of the characteristic decay length of the sensitivity of a nanorod sensor is known to be in the range of 10 nm to tens of nanometers, but the exact value is unknown. As we know, metallic nanostructures possess plasmonic resonances that spatially confine light on the nanometer scale. Does this mean that the sensing abilities of metallic nanostructures are distributed locally? Also, the sensitivities of coupled nanostructures are believed to be higher than those of single nanostructures,12,13 but recent experimental results have not proved this.29 Are the sensitivities of coupled nanorods definitely better than those of single nanorods for plasmonic sensor applications? To answer these questions and to explore the possibility of detecting single biological molecule using LSPR nanosensors, we investigated the plasmonic sensing abilities of individual and coupled gold nanorods theoretically, using the finite-difference time-domain (FDTD) method.3032 In this study, we state several simple rules for the rational selection of nanorod characteristics and also answer the questions we have posed above. The calculation results show which parameters are important in improving nanorod plasmonic sensor sensitivities. We also show Received: August 23, 2011 Revised: October 12, 2011 Published: October 14, 2011 22877
dx.doi.org/10.1021/jp2081066 | J. Phys. Chem. C 2011, 115, 22877–22885
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that a detection limit at the level of a single biological molecule is achievable through nanostructure design. Our simulation results agree with the previously reported experimental results and help in the optimization of plasmonic nanosensors.
’ METHODS The FDTD method is an explicit time-marching algorithm used to solve Maxwell’s curl equations on a discretized Yee spatial grid. It can be used to study both the near- and far-field electromagnetic responses of metal nanostructures of arbitrary shapes. The method enables the computation of the electromagnetic field distribution around a nanostructure and the absorption and scattering cross sections of metallic nanostructures. The FDTD method has been extensively tested and applied in the calculation of LSPR of metallic nanostructures in various dielectric environments. Here the FDTD method is used to calculate the LSPR characteristics of individual or coupled gold nanorods.3032 We take advantage of the rotational symmetry of the system to reduce the problem to two dimensions; this significantly decreases the required memory and computation time. In the calculations, we set the mesh pitch at 0.5 nm, taking into account several factors such as computing burden, convergence, and staircase effects. An electromagnetic pulse is launched near the nanorod. Perfectly matched-layer absorbing boundary conditions are implemented to truncate the computational domain without introducing spurious reflections. The optical dielectric function of the gold material is modeled using a DrudeLorentz dispersion model.33 The refractive indexes of the surrounding media were taken to be 1.33 for water and 1.49 for silica glass. ’ RESULTS AND DISCUSSION Bulk Sensitivity of Individual Gold Nanorod Plasmonic Sensor. First, the LSPR spectra of a single gold nanorod
(diameter 20 nm, length 64 nm, aspect ratio 3.2) are calculated in air (refractive index n = 1.0), water (n = 1.33), and silica (n = 1.49). The spectra for silica-layer-coated nanorods immersed in water are also calculated for different coating thicknesses. Typical results are shown in Figure 1. It is well known that the sensing ability of a LSPR sensor in response to changes in the refractive index can be approximately described by:4,34 λLSPR ¼ λ0 þ m 3 Δn 3 ð1 e2d=ddecay Þ
ð1Þ
where λLSPR is the plasmon resonance maximum of the nanostructure, m is the sensitivity factor, d is the effective thickness of the adsorbate layer, Δn is the difference between the refractive index of the adsorbate and that of the surrounding medium, and ddecay is the characteristic sensitivity decay length of a sensor (which is also relative with the electromagnetic field decay length). When the nanorod is placed in a bulk material, that is, the effective thickness d is infinite, the relation can be simplified to λLSPR ¼ λ0 þ m 3 Δn
ð2Þ
The inset in Figure 1a shows the theoretical plasmon resonance maximum of the nanorod as a function of the refractive index. It fits the plot of eq 2 well. For this, the sensitivity factor m is adjusted to ∼373 nm/RIU (RIU = refractive index unit). This sensitivity is called the bulk sensitivity of the nanorod. The concept of bulk sensitivity can therefore be very helpful because in the first approximation, d ≈ ∞. In practice, biological detection usually occurs within a few to 10 nm for receptorligand or proteinprotein interactions. In the case of a silica coating, the maximum of λLSPR
Figure 1. (a) Spectra of nanorod (rod-20-64) in air (black), water (red), and silica (green) media. The blue curves are the spectra of the nanorod coated with silica layers of thickness 1, 2, 5, 10, and 20 nm in water, in sequence. Inset is the plasmon resonance maximum of the nanorod as a function of the refractive index. (b) Plasmon resonance maximum of the nanorod as a function of the thickness of the coating silica layer (left) and the corresponding differentia (right). The dots are simulated data and the corresponding fitting lines are red curves. The dashed line is the plasmon resonance maximum of the nanorod in the silica medium.
increases with increasing layer thickness and, as expected, asymptotically attains the value found for a pure silica environment. The plasmon maximum of such nanorods, calculated from the spectra in Figure 1a, can be correctly fitted by eq 1. This time, m = 371 nm/ RIU (a value very close to 373) and ddecay= 18 nm is obtained. In this case, the sensitivity of the nanorod sensor decreases exponentially with increasing coating thickness. It is therefore better to place the analyte molecules to be detected in the vicinity of the nanorod to lower the detection limit.28,35 In this paragraph, the diameter of the nanorod is fixed at 20 nm. Only the length of the nanorod is changed to investigate the sensitivity and the characteristic decay length of the nanosensor. Figure 2 shows that the plasmon resonance maximum increases when the length increases and that the sensitivity increases correspondingly. These results correspond to a simple analytical model that also relies on the plasmon resonance wavelength and the sensitivity of the nanorod to the aspect ratio k of the nanorod12,36 sffiffiffiffiffiffiffiffiffi 2πcpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ne2 λLSPR ¼ ð3Þ ε∞ þ kn2m , ωp ¼ ωp ε0 m e ∂λLSPR 2πc knm pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ωp ∂nm ε∞ þ kn2m 22878
ð4Þ
dx.doi.org/10.1021/jp2081066 |J. Phys. Chem. C 2011, 115, 22877–22885
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Figure 2. Plasmon resonance maxima of nanorods with the same diameters (20 nm) in water as a function of the length of the nanorod; the inset shows the characteristic decay length of the sensitivity of the nanorod as a function of the length of the nanorod. The dots are the simulated data and the curved lines are simple data link lines.
In this model, ωp is the bulk plasma frequency of the metal, nm is the environmental medium refractive index, N is the electron density of the metal, ε0 is the permittivity of free space, and me is the effective electron mass. Here the aspect ratio k of the nanorod is in the range of 2.754.2, and our numerical simulation results reveal that λLSPR and the sensitivity of the nanorod increases linearly as a function of the nanorod length. These simulations are only partially in agreement with the analytical model in the sense that the general tendency of λLSPR and that of the sensitivity are given by the analytical model. Our theoretical results agree better with the experimental results reported by Miller and Lazarides. They have observed experimentally that the bulk sensitivity of the plasmonic sensor correlates with the LSPR peak wavelength, regardless of the nanoparticle shape.37,38 The characteristic decay lengths of the nanorod sensitivities, which can also be obtained by our simulations, are shown in the inset of Figure 2. For all nanorods, the decay length is close to 20 nm, that is, the dimension scale of the transverse diameter of the nanorod, and increases slowly with nanorod length. We think that this rule is very helpful in designing and optimizing nanorod plasmonic sensors. To clarify further how to choose the most suitable size or aspect ratio of the nanorods, gold nanorods with different diameters and lengths (nanorods with diameter 10 nm and length 34 nm are denoted as rod-10-34; rod-15-50, rod-20-64, rod-30-88, and rod-40-108 are also studied and have similar aspect ratios, decreasing slightly with size from 3.33 to 2.7) are calculated and investigated in detail. Their plasmon resonance maxima are all calculated at a wavelength close to 735 nm in water. This means that we will compare nanorods showing almost the same plasmon resonance maxima in water but with different aspect ratios. For the smallest and largest nanorods (rod-10-34 and rod-40-108), Figure 3a shows the evolution of λLSPR and of the decay length as a function of the thickness of the silica shell; the nanorod with the smaller diameter has the shorter decay length and consequently the higher sensitivity in the vicinity of the surface. The characteristic decay length is still comparable to the diameter of the corresponding nanorod. Moreover, Figure 3b shows that although the plasmon resonance maxima for these nanorods in water are almost the same, the bulk sensitivity of the nanorod with the larger diameter is higher. It can be concluded that for the aspect ratio used in this study, the nanorod bulk sensitivities are higher for larger diameters. This result is in agreement with a recent experimental report by Wang et al. and cannot be explained by the above simple analytical
Figure 3. (a) Plasmon resonance maxima of nanorods (rod-1034 (red) and rod-40108 (green)) in water as a function of the thickness of the coating silica layer (left), and the corresponding differentia (right). The dashed line is the corresponding plasmon resonance maximum of the nanorod in the silica medium. (b) Characteristic decay lengths of the nanorod sensitivities (rod-1034, rod-1550, rod-20-64, rod-3088, and rod-40108), and the bulk sensitivities of the corresponding nanorods.
model. In their report, the largest nanorod (rod-44-108) exhibits a bulk sensitivity of 326 nm/RIU, that is, about twice the sensitivity (156 nm/RIU) of the smallest nanorod (rod-10-26).14 However, even if the correct trend is indicated by our simulations, there is still a difference between the experimental (156 nm/RIU) and the calculated (256 nm/RIU) sensitivities by us for the smallest nanorod (rod-10-26). We suspect that the sensitivity of the smallest nanorod is not so low and is in reality closer to the calculated value. It should be noted that the calculated bulk sensitivity of the nanorod plasmonic sensor is often higher than the value obtained through experimental measurements.7,14,15,21,28 Apart from certain errors in the numerical simulations (e.g., the optical constant of gold, the mesh size of the simulation), we mainly attribute the deviation to an experimental underestimation of the sensitivity. For instance, the substrate or a surface adsorbate (e.g., a surfactant used during synthesis) could induce a λLSPR red shift, which could hinder access to surrounding molecules with different refractive indexes, or impede replacement of the previous adsorbate when the surrounding medium is changed. Moreover, according to our results for nanorods coated with surfactant adsorbates, nanorods with smaller diameters have shorter ddecay values, leading to greater λLSPR red shifts compared with those of nanorods with larger diameters. It is probable that these factors would result in underestimations of the plasmonic sensor bulk sensitivities, especially for nanorods with small diameters. Our results therefore provide a simple rule for estimating the characteristic decay length for nanorods of different sizes: ddecay is comparable to the diameter of the nanorod. Specifically, ddecay is slightly shorter than the diameter when the aspect ratio of the nanorod is
