ARTICLE pubs.acs.org/JPCC
Computational Prediction of Molecular Photoresponse upon Proximity to Gold Nanorods Jinsong Duan,†,‡ Dhriti Nepal,†,# Kyoungweon Park,†,§ Joy E. Haley,† Jarrett H. Vella,‡ Augustine M. Urbas,† Richard A. Vaia,† and Ruth Pachter*,† †
Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, Ohio 45433, United States General Dynamics Information Technology, Inc., Dayton, Ohio 45433, United States # Universal Technology Corporation, Dayton, Ohio 45433, United States § UES Inc., Dayton, Ohio 45433, United States ‡
bS Supporting Information ABSTRACT: We endeavor to gain insight into radiative and nonradiative decay phenomena of emitters proximate to gold nanorods (AuNRs), which could be useful in fluorescence enhancement and also in mitigating loss in metal nanostructures. Factors that influence the photoresponse, such as the orientation, positioning, and distance, were quantified by applying finite-difference time-domain simulations, particularly for small separations afforded by chemical synthesis of the nanoparticles. In order to provide guidelines to experimental work, the geometries examined were consistent with synthesized nanostructures. For fluorophore fluorescence enhancement (FFE), we quantified requirements for compensation of the large nonradiative decay at small separations to the AuNR surface, for example by the preferable use of larger aspect ratio rods, yet care has to be taken in utilizing larger nanostructures. Quantifying the quantum yield is important in assessing the interplay among various parameters that tune the fluorescence. For example, although placing an emitter at the tip of the AuNR at relatively close proximity may offer increased FFE, the effect was opposite for the larger aspect ratio AuNR. Moreover, the possible role of the quadrupolar mode on nonradiative decay was quantified for different aspect ratio AuNRs. AuNRs’ surface roughness was shown to increase the radiative decay rate, and the immersive medium can have a large effect on fluorescence enhancement. For the range of AuNRs considered, tunability provides FFE enhancements of about 10%; however, it significantly increased when using emitters with small intrinsic quantum yields. Finally, assemblies of AuNRs demonstrated large nonradiative decay in cases of small separation between the nanorods.
’ INTRODUCTION As has been recently pointed out,1 a “publication storm” describing new developments in the investigation of plasmonic nanostructures is emerging, including colloidal synthesis of noble metal gold and silver nanoparticles, fabrication by electron-beam lithography, characterization, and computational prediction. Applications using plasmonic nanoparticles range from surface enhanced Raman spectroscopy2 to single-molecule fluorescence enhancement, as observed for example by Kinkhabwala et al. for bowtie-like nanostructures.3 This phenomenon was suggested in the pioneering work of Purcell.4 The ability to improve molecular emission in proximity to a metal nanoparticle was recently assessed to have an important influence on a number of emerging areas,5 including biological applications,6 or in the use of quantum dots with biomolecular linkers.7 Plasmonic emission enhancement from quantum dot monolayers in the vicinity of Ag nanoprisms was also shown.8 Moreover, careful design for nonradiative energy transfer could assist in improvement of losses in metal optical metamaterials.9 In addition, enhancement of two-photon absorption of chromophores proximate to a nanoparticle, r 2011 American Chemical Society
although postulated experimentally,10 is still not fully understood, and an understanding of associated phenomena could have a tremendous impact on optical applications. Three-photon absorption enhancement by silver nanoparticles’ two-photon absorption was recently demonstrated11 as well as metal-enhanced phosphorescence.12 Understanding design parameters that will result in fluorescence enhancement will be the first step toward realizing these goals. However, gaining insight into the molecular photoresponse upon close proximity to a nanostructure’s metal surface for materials that have been chemically synthesized has been difficult because of the number of parameters that determine radiative and nonradiative decay rates. Previously, properties of an emitter interacting with small metal nanoparticles, specifically spheres or spheroids described analytically, were investigated in detail within the quasi-static approximation by Gersten and Nitzan.13 The photoresponse was Received: September 24, 2010 Revised: June 13, 2011 Published: June 30, 2011 13961
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The Journal of Physical Chemistry C analyzed regarding molecule nanoparticle distance, the relative orientation, and nanoparticle shape, which was sufficient in analyzing early experiments.14 More recently, fluorescence enhancement by nanoshells and nanorods was reported,15,16 while incorporation of more than one nanoparticle was also investigated.17 Notably, metal nanorods, extensively studied by Murphy et al.,18 are of particular interest because of greater versatility, such as in placing the fluorescent moiety at specific locations. The spectral tunability provided by changing the metal nanorod’s aspect ratio (R)19 can have advantages in reducing background fluorescence and scattering. Reduction of the plasmon dephasing in rods as compared to spheres was also observed.20 In this work, prediction of radiative and nonradiative decay of a molecular emitter close to gold nanorods (AuNRs) is of interest. Quantitative analyses and a better understanding of the photoresponse for metal nanorods with emitters at close proximity, which will provide guidance for chemical synthesis, are still lacking, and discrepancies between predicted and observed responses noted. This is especially important in the use of single and self-assembled AuNRs fabricated by seed mediated growth with fluorophore adsorption, which result in relative close proximity of the emitter to the nanostructure. Such approaches can yield particles of high purity with specific shape, size, and preferential molecular binding and enable control of the molecular emission phenomenon.21 However, although radiative decay processes were addressed to some extent, nonradiative decay phenomena are still not well quantified. This is an important consideration upon close proximity to the AuNR and was shown even for spheres; for example, calculations for a sphere using the system’s dyadic Green’s function within the dipolar approximation emphasized the importance of rigorous prediction.22 Quantifying the factors that affect fluorophore fluorescence enhancement (FFE) for realistic AuNR nanostructures will ensure that, despite quenching, designs can be fabricated that still provide emission enhancement. For instance, importance of the separation of the gold nanoparticle from the human blood protein was demonstrated.23 The probability of spontaneous emission as given by Fermi’s golden rule is proportional to the transition dipole moment and electromagnetic local density of states (LDOS),24 which require accurate calculations for realistic nanorod geometries. To gain an understanding of parameter space influencing the photoresponse of an emitter proximate to AuNRs based on our synthesized nanorod structures,25 finite-difference time-domain (FDTD) simulations solving Maxwell’s equations were performed, with the molecule modeled as an oscillating dipole source. We examined quantitatively the dependence of the quantum yield on the AuNR’s aspect ratio. For example, we have shown that although placing the emitter at the tip of the AuNR at relatively close proximity may offer a slight increase in its value, the effect is opposite for the larger aspect ratio AuNR, although such nanostructures generally provide a larger field enhancement. The excitation of the quadrupolar mode provided insight into the behavior of hybrid materials, analyzed also as a function of the aspect ratio. Moreover, suppositions regarding self-assembled AuNRs were derived, which will enable in future work rational design of fluorophore AuNR systems with an optimized emitter emission.
’ COMPUTATIONAL DETAILS FDTD simulations were performed with the Lumerical software package,26 using the Yee algorithm, as is described elsewhere.27
ARTICLE
Figure 1. A dipole oriented (a) parallel to the long axis of the AuNR (length L, including the hemispheres, diameter D), positioned in the center, and (b) perpendicular to the tip of the AuNR. The separation d is in nm.
The propagation of the electromagnetic field is defined on a spatial grid through consecutive time steps, and the spectrum was obtained from a single run. To ensure accuracy, the grid size was set to 0.5 nm in all dimensions, unless mentioned otherwise. The time step was determined by increments according to the time stepping stability criterion,28 and the simulation time was estimated so that the field components decayed to nearly zero. Size correction to the bulk mean collision rate of the conduction electrons is necessary for nanoparticle sizes comparable to the mean free path of the electrons because of collisions to the surface. This is achieved by a modified expression for the collision rate γ, namely, γ = γ∞ + AνF/r, where γ∞ is the value in bulk metal, νF the Fermi velocity in bulk metal, and A a geometric parameter that relates the mean electron free path to the particle’s average radius r. Experimental data characterized for thin films29 were fitted to the dielectric function, where an expansion of Lorentzian terms was included to account for interband transitions and the other non-Drude contributions,30 as mentioned, assuring a best fit in the simulated spectral region. The explicit demonstration of the equivalence of the timedomain equations to those in the frequency domain using analytical forms of the dielectric function have been described in detail by Gray et al.31 The emitter was described by a dipole source oscillating at the emission frequency, representing a two-level transition dipole moment in free space, unless otherwise discussed. The simulated orientations are shown in Figure 1, with the emitter placed at various distances from the AuNR, which was modeled as a cylinder capped with half-spheres. Fluorophore adsorption at the long axis can provide a larger adsorption surface area, and thus positioning at the AuNR’s long axis was assumed. Although preferential binding at an AuNR tip was demonstrated,32 no comparison to alternative fluorophore positioning was reported. The fluorescence quantum yield Y was defined by Y = Γr/(Γr + Γnr), where Γr and Γnr are the radiative (r) and nonradiative (nr) decay rates of the emitter, respectively. The quantum efficiency enhancement factor fY, i.e., fY = fr/[(1 Γ0) + Γ0(fr + fnr)], also takes into account the intrinsic fluorescence quantum efficiency of the emitter, Γ0 (ratio of emitted to absorbed photons). In this work, Γ0 was assumed to be 1. The radiative fluorescence enhancement factor is defined by fr = Γr/Γ0, where Γr/Γ0 = Pr/P0. Pr is the calculated radiative power normalized to P0, which is the power radiated by a dipole in a homogeneous 13962
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The Journal of Physical Chemistry C medium, given by an analytical expression, as the LDOS depend on the refractive index. The radiative power was derived by Fourier transformation of the time-dependent electromagnetic field, constructing the frequency-dependent Poynting vector. Radiative decay rates were calculated from powers obtained from the surface integral of the system that included the dipole and the AuNR (described by six frequency domain power monitors that defined a box around the system). The nonradiative decay factor was defined by fnr = Γnr/Γ0, where Γnr/Γ0 = Pnr/P0. The nonradiative power was calculated from the difference of the total power emitted by the classical dipole and the radiative power.
’ RESULTS AND DISCUSSION In this work we considered AuNR geometries that we synthesized25 and span a range of aspect ratios. Such an approach enables estimates of the FFE for realistic AuNRs that do not always follow a systematic change in the geometry, therefore providing a practical route toward FFE optimization. FDTD simulations for a system that included an AuNR or an AuNR assembly and an emitter model were carried out. We based the calculations on AuNRs with aspect ratios of 2.9 and 6.5 (L, D = 56, 19.2 nm; L, D = 81, 12.5 nm, respectively), having local surface plasmon resonances (LSPRs) of 608 and 861 nm, respectively. The red-shift for the larger aspect ratio AuNR can be qualitatively explained by a decrease of the depolarization factor.25 Specifically, following Gans’s analytical derivation for ellipsoids33 (ref 1 and references therein), the dipolar polarizability is proportional to the so-called depolarization factors, defined in terms of the principal axes of the ellipsoid, dependent on the aspect ratio. Because of the inverse proportionality of ε to the depolarization factor at resonance, larger real ε at red-shifted wavelengths are required as the depolarization factor decreases, namely as R increases. This qualitative description also rationalizes a red-shift with an increase of n.34 Indeed, the LSPRs we report for the two aspect ratios considered differ from those we reported previously because effects of the immersive medium were treated separately in this work (n = 1), in order to facilitate comparison with related results, e.g., as derived analytically.13 Results of the changes in the fluorescence quantum yield Y (%) are summarized in Table 1. To ensure that no important discrepancies due to different volumes occurred, we compared the results with those for AuNRs having the same volume as those of R = 2.9. For R = 6.5, an increase in Y by ca. 10% was noted (d = 2 nm, parallel orientation, see Table S1). The nonradiative power is proportional to the volume, while the radiative power to its square, as based on the analytical derivation, and thus the relative increase can be qualitatively rationalized. In the following, we discuss changes in Y for AuNRs with R = 2.9 and 6.5, and for comparison, results for an AuNR with R = 14.5 (L, D = 145, 10 nm)25 are given. The most important consideration in optimizing the FFE is the relative orientation of the emitter to the AuNR. Because the local field enhancement under a transverse polarization excitation (perpendicular orientation of the emitter to the AuNR long axis) is small, it can be assumed that the FFE depends primarily on the longitudinal excitation (parallel orientation) in a sample with random orientations. Indeed, since calculated Y were
