Fluorescence Enhancement of Chromophores Close to Metal

J. Phys. Chem. C 2009, 113, 121–133

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Fluorescence Enhancement of Chromophores Close to Metal Nanoparticles. Optimal Setup Revealed by the Polarizable Continuum Model Sinisa Vukovic,† Stefano Corni,‡ and Benedetta Mennucci†,* Department of Chemistry and Industrial Chemistry, UniVersity of Pisa, Via Risorgimento 35, 56126 Pisa, Italy, and INFM-CNR National Research Center on nanoStructures and bioSystems on Surfaces (S3), Via Campi 213/A, 41100 Modena, Italy ReceiVed: September 12, 2008; ReVised Manuscript ReceiVed: NoVember 3, 2008

A direct estimate of changes in the radiative and nonradiative decay rates of a chromophore near metal nanoparticles is obtained using a quantum mechanical description coupled to the polarizable continuum model. The results account for experimentally observed continuous change from decreased to increased fluorescence. The changes are described as the effects of a dependence on the distance and orientation between the chromophore and the metal nanoparticle, as well as the size, shape, number, and type of the metal particles and the influence of the solvent. The chromophore investigated was N,N′-dimethylperylene-3,4,9,10dicarboximide in combination with silver and gold particles. The study explains and rationalizes how intrinsic characteristics of the metal predetermine the nanoparticle’s behavior toward chromophore excitation and decay rates. As a result, the optimal setup (shape, position, orientation) that gives the largest enhancement is revealed. 1. Introduction A molecule in the vicinity of a metal surface or a metal nanoparticle (MNP) can exhibit different optical properties from an isolated molecule. This was experimentally demonstrated already in the 1960s by the works of Drexhage et al.1 for fluorescence lifetimes of chromophores close to a planar metal surface, and theoretical modeling of the system (based on classical electrodynamics) was soon available (see ref 2 and references therein). These works pointed to the quenching power of metal surfaces at short metal-molecule distances, i.e., to a metal-induced weakening of the fluorescence signal. In the 1970s, it was discovered that (rough) metal surfaces and nanoparticles can amplify molecular optical properties (i.e., strengthen the experimental signal), notably Raman scattering,3 and the term surface-enhanced Raman scattering (SERS) was coined. The importance of electromagnetic effects was recognized soon thereafter.1,4 The ambiguous nature of the effect of metals on optical molecular properties (strengthening or weakening them) was already evident, although it could be due to the different addressed properties (fluorescence vs Raman scattering), as well as the different metal specimens (flat surfaces vs rough surfaces or colloidal nanoparticles). Currently, the ambiguity in the effect of metals on molecular fluorescence is more striking: Some experiments performed on a chromophore adsorbed on metal nanoparticles reported fluorescence quenching;5,6 others on the same kind of system found fluorescence enhancement7-10 (a phenomenon dubbed surface-enhanced fluorescence, SEF). Part of the contradiction might originate in the use of different quantities to estimate fluorescence efficiency: sometimes, the fluorescence quantum yield (number of emitted photons per number of absorbed photons) is used, whereas in other cases, discussions are based * Corresponding author: [email protected]. † University of Pisa. ‡ INFM-CNR National Research Center on nanoStructures and bioSystems on Surfaces (S3).

on the fluorescence intensity at constant exciting intensity (or the related relative brightness, defined in a subsequent section). Whereas the former is not sensitive to the effect of metals on molecular absorption, the latter does account for such effects. This possibility notwithstanding, the apparently contradictory results might arise because the effects of metals are very sensitive to the details of the system: the chemical nature of the metal, the particle shape and size, the position and the orientation of the chromophore with respect to the particle, and the environment in which the fluorescence process takes place (e.g., supported on surfaces, in water). For example, it has been demonstrated that one can switch between quenching or enhancement of the fluorescence brightness by varying just the metal-molecule distance.11 A careful analysis of the effects of all the experimental variables in play would be useful to find conditions that favor fluorescence enhancement or quenching. It is clear that identifying these conditions is of broad interest, because of the potential utility of metal-affected fluorescence in analytical and biosensing applications,12 electronics,13 and materials science,14 to cite just a few interested fields. From the theoretical point of view, different groups have focused on the problem of calculating changes in molecular properties due to nearby metal particles especially for SERS. (See a recent review on the subject15 for an updated summary of the literature.) However, a comprehensive quantum mechanical report that addresses the effects of all of the various parameters mentioned above on the fluorescence quantum yield and relative brightness is, to the best of our knowledge, lacking. In addition, in computational simulations of metal-affected fluorescence, the point-dipole approximation is invariably used. From a chemical point of view, approximating the chromophore as a point dipole is a quite drastic assumption; it is particularly questionable for molecule-metal distances that are comparable to the chromophore size. The aim of this work is to provide a comprehensive account of the various conditions that give rise to fluorescence quenching or enhancement, giving a rationale for the apparently contradictory results ranging from strong quenching to strong enhance-

10.1021/jp808116y CCC: $40.75  2009 American Chemical Society Published on Web 12/11/2008

122 J. Phys. Chem. C, Vol. 113, No. 1, 2009 ment and suggesting optimal setups for obtaining the largest fluorescence enhancement. Such an account is based on a quantum mechanical (QM) treatment of the chromophore and a continuum dielectric description of the metal specimen16,17 and the surrounding environment.18,19 Notably, our model is not limited to single spherical metal particles, but can address complex shapes and a variable number of particles. It is also clear that the level of description of the molecule is much more chemically sound than that of a point dipole, and in principle, it does not require any molecular input aside from the molecular structure. Finally, the same QM model can describe both radiative and nonradiative decay rates using a single coherent picture. In particular, we present calculations of fluorescence quantum yield and relative brightness for a realistic chromophore [N,N′dimethylperylene-3,4,9,10-dicarboximide, or perylene diimide (PDI)] on metal nanoparticles (MNPs) of different shapes (spheres, union of spheres), sizes, and chemical natures (Au or Ag) and immersed in different environments (in vacuo or water solutions), and we rationalize the different trends (enhancements, quenching, efficiency) in terms of the underlying physical phenomena (radiative and nonradiative decays, excitations of the MNP plasmons). The article is organized as follows: In section 2, the model used to perform the calculations is summarized, and all of the investigated physical quantities are defined. In section 3, results for different chomophore-nanoparticle systems are presented and discussed with respect to metal shape, size, and nature; orientation; and solvent. Finally, in section 4, conclusions are drawn. 2. Methods 2.1. Definitions of the Investigated Quantities. To describe the overall influence of the metal on the photoinduced molecular fluorescence, it is necessary to model the effect of the metal on different processes: (i) The first step is the absorption of exciting light by the molecule, whose rate determines the probability that the molecule is indeed in the excited state and thus available for emission. This process is characterized by the absorption coefficient A. (ii) Once in an excited state, the molecule undergoes internal processes (e.g., internal conversion, relaxation) that brings it into the emitting excited state. Although the metal might affect these processes as well, they are usually very fast (at least for fluorophores) compared to the other phenomena under investigation, and we shall not consider them further in this work. (iii) When the molecule is in the emitting excited state, it can decay to the ground state by emitting a photon (radiative decay rate Γrad) or nonradiatively (nonradiative decay rate Γnonrad). The metal affects Γrad; creates new channels of nonradiative decay (energy and charge transfers from the molecule to the metal); and in principle, can also affect the intrinsic nonradiative decay of the molecule, although this is probably hidden by the prevalence of the new metal-enabled decay channels. The effectiveness of nonradiative decay via metal-molecule charge transfers decreases exponentially with the metal-molecule distance. Thus, it might be relevant for chromophores that are chemically bound to the metal particle by short molecular spacers. The quantities that summarize the effects of a metal on these processes are the fluorescence quantum yield, ΦFQY, and the relative brightness, ΦRB. Fluorescence quantum yield is defined as

Vukovic et al.

ΦFQY ) Γrad/(Γrad + Γnonrad)

(1)

ΦFQY is the number of fluorescence-emitted photons per number of absorbed photon and represents the fluorescence efficiency at constant absorption. The relative brightness is useful to quantify metal-induced enhancement or quenching of the fluorescence at constant excitation intensity (a condition often used in reports dealing with surface-enhanced fluorescence), and it is defined as

ΦRB ) ΦFQYA/Afree

(2)

where Afree is the molecular absorption coefficient in the absence of the metal. The ratio A/Afree accounts for the different population in the excited state induced by metal effects on the molecular absorption: if, for example, the metal enhances the molecular absorption, more molecules will be present in the excited state and will thus be available for emission. This contributes to the enhancement of the fluorescence intensity, notwithstanding the direct metal effects on Γrad and Γnonrad. Because, in general, the metal affects A (in addition to Γrad and Γnonrad), one indeed expects ΦRB * ΦFQY. 2.2. Model. We have developed a method to directly estimate A, Γrad, and Γnonrad due to nearby metal particle(s) and therefore rationalize the observed quenching or enhancement of fluorescence in terms of separate contributions from the influence of the metal and/or solvent. This method is based on a focused model in which the metal is considered as a continuous dielectric characterized by the experimental metal optical constants and the chromophore is treated quantum mechanically. Here, we provide only a short summary, as a detailed description of the method can be found in refs 16 and 17. The model belongs to a family of methods known as polarizable continuum model (PCM), which was originally formulated to treat molecules in solution but, in subsequent years, has been extended to a variety of more complex surroundings such as liquid crystals, ionic solutions, gas/liquid (or liquid/liquid) interfaces, and the present case of metal nanoparticle(s) plus a solvent. A detailed summary of this family of methods can be found in ref 18. Within such a framework, the ground-state interaction between the molecule and the metal is electrostatic in nature, and it is due to their mutual polarization. In particular, the molecule is described by an effective Hamiltonian obtained by adding the in vacuo electronic Hamiltonian and the electrostatic interaction energy between the molecular charge density (nuclei + electrons) and the polarization of the metal induced by the molecular charge density itself. Such a polarization is conveniently expressed in terms of apparent charges placed on the metal surface (and on the surface of the molecular cavity hosting the chromophore as a solute if in the presence of a solvent). The apparent charges are obtained as the boundary element method (BEM) solution of the integral equation formalism (IEF) approach to the Poisson problem.19 We also remark that this polarization is calculated by considering the metal as a perfect conductor (and a solvent as a standard dielectric). The electronic excitation energies and transition densities of the molecule are calculated within a linear response approach [time-dependent Hartree-Fock (TD-HF), time-dependent density functional theory (TD-DFT), but also semiempirical single configuration interaction methods such as Zerner’s intermediate neglect of differential overlap (ZINDO) can be viewed as approximate response function methods]. In this case, in the response function equation that determines molecular excitation energies and transition densities, one adds a term that represents

Fluorescence Enhancement of Chromophores Close to MNPs

J. Phys. Chem. C, Vol. 113, No. 1, 2009 123

the interaction of the transition density with the oscillating metal (and solvent) polarization induced by the transition density itself. This interaction is again described with the IEF-BEM procedure used for the ground-state Hamiltonian. In the present case, however, the frequency-dependent dielectric permittivity of the metal (and the solvent) is used. (The frequency is chosen to be equal to that of the studied molecular electronic transition.) For the metal, this quantity is, in general, complex; as a result, the excitation energies, ω, are complex as well. In ref 17, it is explained that the imaginary part of these excitation energies is related to the (finite) lifetime of molecular excited state due to the transfer of the molecular excitation to the metal (and its following dissipation). As the decay rate can be defined as the inverse of the lifetime, we have

present model. For example, the metal response is assumed to be local, but nonlocality effects could contribute to molecular decay rates in nonobvious directions. (For example, Γnonrad decreases when nonlocality is considered at the hydrodynamics level,21 but it increases when the more accurate Lindhard dielectric constant is used.17) Moreover, the additional Drudemodel scattering due to metal particle surfaces is known to be dependent on the particle’s surroundings.22 The presence of a surface combined with the nonlocal metal response could give rise to additional dissipation mechanisms.23 Although these effects surely deserve further studies (work on these subjects is ongoing in our laboratory), we note that models for metals such as ours (and even simpler in the description of the molecule and the shape of the MNP) have provided good agreement with experiments, appearing to be accurate enough to grasp the physics behind the problem of fluorescence quenching vs enhancement. 2.3. Computational Details. Present estimates of radiative and nonradiative decay rates are based on quantum mechanical calculations within the integral-equation-formalism version of the polarizable continuum model (IEFPCM). More details on the model have been reported before.19 The QM method of choice for the study of absorption and fluorescence was Zerner’s intermediate neglect of differential overlap (ZINDO) method,24 which we previously tested17 against TD-DFT and found to be equally as reliable but dramatically faster in predicting experimentally observed fluorescence data. All calculations were performed on a locally modified version of Gaussian 0325 suite of programs. The geometries of the chromophore (N,N′-dimethylperylene3,4,9,10-dicarboximide or perylene diimide, PDI) in its ground and excited states were obtained by the B3LYP and CIS methods with the 6-31+G(d) basis set. In the calculations including the effects of the solvent, the chromophore was enclosed in a single cavity made up of a combination of spheres centered on C, O, N, and CH3 with radii 1.925, 1.830, 1.750, and 2.525 Å, respectively. The solvent (water) was represented by its static dielectric constant, ε ) 78.39, and by its optical dielectric constant, ε∞ ) 1.776. The metal was treated classically as a dielectric with a local, frequency-dependent permittivity taken from experimental data, corrected for the limited mean free-path according to the Drude model26

Γnonrad ) -2Im{ω}

(3)

Remarkably, no dipole approximation is assumed to describe this chromophore-metal transfer. The coupling that determines such a transfer is, in fact, calculated considering the interaction of the quantum mechanically obtained transition density of the chromophore with the oscillating electromagnetic field produced by the corresponding metal polarization, which, as said before, is represented in terms of apparent charges spreading on the whole surface of the MNP. It has to be noted that the BEM procedure used is valid only in the quasistatic (or nonretarded) limit (i.e., we approximated Maxwell equations with the Poisson equation, which is valid in the limit where all the distances and sizes in the studied system are much less than the wavelength λ), which the investigated system PDI-NP well satisfies. The generalization of BEM to the retarded equations has been demonstrated before.20 The absorption coefficient, A, and the radiative emission rate, Γrad, are given by16,17

A)

2π b 2 |µK0| 3p2cn

(4)

4ω3n b 2 |µK0| 3pc3

(5)

Γrad )

where b µK0 is the transition dipole between the ground state and the Kth excited state and n is the refractive index of the medium in which absorption/emission takes place. In addition to the fact mol , is directly affected by that the molecular transition dipole, b µK0 the interaction with the metal (and with the solvent, if present), the metal (and the solvent) also give rise to explicit terms in eqs 4 and 5, because b µK0 should include the dipoles induced in the metal (and in the solvent) by the molecular transition density

{(

2 εmet(ω,R) ) εmet exp (ω) + Ω

1

i ω ω+ τ

-

)

1 (R + VFτ) ω ω+i τR

[

]}

(6)

(7)

Once these basic quantities (Γnonrad, Γrad, A) have been calculated, ΦFQY and ΦRB are accessible via eqs 1 and 2. The enhancement of A and Γrad is often discussed in the plasmonics literature as the result of the amplification of the incident (A) or moleculeemitted (Γrad) field due to the field interaction with the metal nanoparticle. Equations 4- 6 offer, in the quasistatic case, a different (but equivalent) view of the phenomenon. The equivalence is based on the symmetry properties of the electrostatic Green’s function. The advantage of using eqs 46 is that they do not require additional inputs beyond those already available from PCM response function calculations (e.g., no need to explicitly compute the interaction of the molecule with the total electromagnetic field acting on it). Before moving to the presentation and discussion of the results, it is important to recall the possible limitations of the

where R is the radius of the metal particle, Ω is the plasma frequency (0.332 for silver and 0.293 for gold), τ is the bulk relaxation time (1320 for silver and 306 for gold), and VF is the Fermi velocity (0.64 for silver and 0.64 for gold). All values (reported in atomic units) were extracted from the set of experimental data reported in the compendium by Palik.27 The geometry of the metal nanoparticle was taken to be spherical or a combination of two or three spheres fused along the center-center axis at the distance of their radii. The geometries of PDI-MNP complexes were set up in different orientations and distances with varying radius, number, shape, and type of metal. Orientations were longitudinal (along the long axis of perylene), transversal (along the short axis), and perpendicular (normal to the plane containing perylene). See Figure 1 for a graphical representation of the different PDI-

mol met sol µb K0 ) µb K0 + µb K0 + µb K0

124 J. Phys. Chem. C, Vol. 113, No. 1, 2009

Figure 1. Orientations of metal nanoparticles relative to the chromophore: (L) longitudinal orientation along the long axis of the chromophore, (T) transversal orientation along the short axis, and (P) perpendicular orientation normal to the plane of the flat chromophore.

MNP systems studied, and see Figure 2 for the general setup for the longitudinal orientation. In Figure 2, the distances from the chromophore to the metal surfaces are marked d1 and d2; the radii and centers of the spherical metal particles are r1, r2 and c1, c2, respectively; and the coordinates of the metal spheres are set on the x, y, and z axes as the orientations L, T, and P, respectively. In the present study, the distances of the chromophore (from C of CH3 for the longitudinal orientation, from H of aromatic CsH for the transversal orientation, and from the plane of the molecule for the perpendicular orientation) to the surface of metal particle varied from 3 to 200 Å. The radii of the metal spheres varied from 5 to 250 Å. Values of dielectric constants for metal particles were taken from ref 26 using the experimental absorption and emission frequencies of PDI, 0.08847 au (λ)515 nm) and 0.08678 au (λ)525 nm), respectively (where the values refer to an n-heptane solution28): Re{εmet} ) -9.408 (Ag) and -4.125 (Au), Im{εmet} ) 0.798 (Ag) and 2.578 (Au) for the absorption process; Re{εmet} ) -9.906 (Ag) and -4.329 (Ag), Im{εmet} ) 0.813 (Ag) and 2.140 (Au) for the emission process. 3. Results and Discussion This section begins with a preliminary discussion on the behavior of A, Γrad, and Γnonrad for PDI close to a single gold sphere. The section is then divided into four parts on the effects of the orientation, distance, and size of metal particle; the shape and number of metal particles; the type of metal particle; and the solvent. In the final part, an analysis of the MNP polarizability is presented so as to have a more direct connection between the intrinsic properties of the MNP(s) and the changes in the rates of absorption and emission of the chromophore. 3.1. General Trends for Radiative and Nonradiative Rates. We start our report by discussing the qualitative trends of Γrad, Γnonrad, and A for PDI at different distances from one gold spherical nanoparticle. These are the basic ingredients of ΦFQY and ΦRB, and their relative trends are thus the background needed to understand fluorescence quenching or enhancement and help rationalizing results for ΦFQY and ΦRB that we present in the following sections. Remarkably, the trends of these quantities for different numbers or shapes of particles, different metals, and so on are qualitatively similar to the trends presented

Vukovic et al. here. We also verified that the trends of A and Γrad are quite similar (absorption and emission frequencies are close); thus, we do not report the results for A. In our model, the orientation of the metal particle with respect to the chromophore can be arbitrarily chosen. We placed metal particles in L, T, and P orientations, but we report results just for the L and T orientations, as the T and P results are very similar. The results for Γrad and Γnonrad are shown in Figure 3. Consider first the Γrad results. The strongest effect on the radiative decay rate with respect to the free molecule is observed in the longitudinal orientation. Such a result is expected from eqs 5 and 6, which show that the emitting dipole is the vector sum of mol , and the dipole induced the chromophore transition dipole, b µK0 met mol µK0 in the metal particle, b µK0 . In fact, at the studied frequency, b met and b µK0 are parallel for L and their magnitudes add, whereas they are antiparallel for T (and P), thus lowering the magnitude of the total dipole moment upon their addition. Such an effect was noted theoretically in ref 17 for a coumarine dye close to a silver particle, and its experimental observation was reported in ref 29, where it was dubbed phase-induced radiative rate suppression. The effect of distance from the metal particle on the radiative decay rate is also shown in Figure 3. For L, the rate decreases with distance, whereas for T (and P), it exhibits a much less regular behavior, presenting a minimum for a certain distance. Eventually, Γrad for the L and T orientations converge to the value for the free molecule. One can account for such a peculiar trend by referring again to eqs 5 and 6: From these equations, mol met 2 mol 2 met 2 bK0 + b µK0 | ) |µ bK0 | + |µ bK0 | + one can see that Γrad ∝ |µ mol met mol met µK0 . For L, it is a sum of positive terms (µ bK0 · b µK0 > 0), 2µ bK0 · b met (i.e., with thus monotonically decreasing with decreasing b µK0 mol met ·b µK0 increasing metal-molecule distance), whereas for T, b µK0 < 0, and the behavior is not monotonic, presenting a minimum met mol ≈ -µ bK0 . for b µK0 The radius of the metal particle affects Γrad at all distances. This can be understood on the basis of a simple model of the system: an oscillating point dipole close to a metal sphere. In fact, the dipole induced in the metal is proportional to the particle met µK0 increases with polarizability,30 which behaves as R3; i.e., b increasing R. This also explains why the minimum of Γrad for the T orientation shifts at longer distances with increasing R: met mol close to -µ bK0 . the condition for the minimum is to have b µK0 met Because the magnitude of b µK0 increases with increasing R and met decreases with increasing d, to keep the same relationship b µK0 mol ≈ -µ bK0 with increasing R, one should simultaneously increase d. For Γnonrad, the orientation of the molecule did not make a qualitative difference. The trend of Γnonrad with distance can also be understood by referring to the simple but useful point-dipole model close to a metal sphere. On the basis of this model, one expects that, for molecules very close to the metal particle (d , R), the metal behaves as an infinite planar metallic surface. The dependence of Γnonrad on the sphere radius is thus lost, and Γnonrad decays as 1/d3. For large distances (d . R), but still in the quasistatic regime (d , λ) a Fo¨rster-like 1/d6 behavior is expected. These scenarios are presented as a solid line in Figure 4. To assess the quality of this almost universally used pointdipole approximation versus our complete quantum mechanical treatment of the molecule, it can be useful to extract the trends in the two extreme regimes (d , R and λ . d . R) from our quantum mechanical calculations. The points in Figure 4 are the numerically calculated derivatives of ln(Γnonrad) with respect to ln(d), plotted as a function of d. This derivative is -3 in the case of 1/d3 behavior and -6 for the 1/d6 decay. We present



Figure 2. Calculation setup of the chromophore-metal particle system. Each distance, d1 and d2; radius, r1 and r2; and orientation, x, y, and z axes, of the metal particle(s) can be independently varied, in vacuum or solvent, with different numbers and different shapes (fused spheres) of particles for different types of metals.

Figure 3. Logarithm of (top) radiative and (bottom) nonradiative decay rates (s-1) of the chromophore with distance from a metal particle of varying radius in the (left) longitudinal and (right) transversal orientations.

this calculation only for R ) 40 Å, a radius that allows a range of different decay exponents to be observed within the studied range of distances. It is clear that, for distances greater than 20 Å (comparable to the molecular size), the point-dipole model adequately reproduces the quantum mechanical behavior. However, for smaller distances, the quantum mechanical results decay more rapidly than predicted by the point-dipole model. This is likely due to the modification of the molecular ground state due to the metal-molecule mutual polarization and to the metal-molecule coupling via transition multipoles higher than the dipole, effects that are not present in the point-dipole model. Incidentally, Figure 4 also shows that assuming a Fo¨rster-like 1/d6 decay of the metal quenching efficiency is justified only for d . R.

3.2. Effects of Distance from and Size of a Gold Particle on the Fluorescence. In Figure 5, we report the influence of distances and radii on the fluorescence quantum yield and the relative brightness for PDI in the L orientation. In these graphs one can see the overwhelming influence of the nonradiative decay rate, which leads to a large quenching of the fluorescence at all values of distances and radii. However, significant differences are observed between ΦFQY and ΦRB, particularly for large radii and long distances. As shown in Figure 3, the effects of distance from the metal particle on Γrad (and A) and Γnonrad have qualitatively similar trends for all three rates: the shorter the distances, the higher the rate. However, in the region of short distances, Γnonrad is of a much greater magnitude than Γrad, so it determines the


Figure 4. Exponent of the Γnonrad decay as a function of the distance from a gold sphere of radius 40 Å. (s) Results for an oscillating point dipole close to the gold sphere, (b) results from our quantum mechanical calculations.

quenching of the fluorescence yield ΦFQY. Even the enhancement of A at short distances is not able to offset the large quenching of ΦFQY, resulting in a ΦRB value smaller than 1. In the region of long distances, the influence of the metal decreases, which decreases all of the rates. For long distances and small radii, ΦFQY and ΦRB thus trivially approach the free-molecule limit, i.e., 1. However, a marked difference between ΦFQY and ΦRB can be seen in the region of long distances and large radii. Here, ΦRB is larger than ΦFQY (although smaller than 1), and it increases with increasing particle radius As noted in the previous section, the effects of the radius of the metal particle for small metal-molecule distances differ for Γrad and Γnonrad. Larger radii maximize Γrad (and A) but are ineffective with Γnonrad. This means that it should be possible to increase Γrad independently of Γnonrad and to produce a relative increase in ΦFQY and an even more pronounced increase in ΦRB (more pronounced because of the simultaneous increase of Γrad and A). These trends are indeed observed in Figure 5. Although, in principle, they can lead to an overall enhancement of the relative brightness for sufficiently large particles, one should not forget that, when R becomes comparable with λ, retardation effects become important and lead to other sources of fluorescence losses (e.g., scattering, retardation damping). Before moving to the further analyses, we note that, even for the free molecule of PDI, the value of ΦFQY is very high. Thus, upon addition of a metal NP, the eventual increase in yield cannot pass 1 by definition (and it is already close to 1), so it will not be as remarkable as the change for ΦRB. For this reason, from now on, the effect of MNP(s) is focused on ΦRB only. In particular, in the following sections, the changes in ΦRB are analyzed with respect to shape, number, and nature of MNP(s). 3.3. Effects of Shape and Number of Metal Particles. In Figure 6, we report ΦRB values of different systems in which the NP is formed by two fused (2F) and three fused (3F) spheres and in which two NPs are introduced. In Figures 7 and 8, the relative values of Γrad and Γnonrad with respect to those for the single-sphere NP are reported. First, we consider changing the shape of an MNP by fusing two and three spheres. By comparison with the single-sphere case, it can be seen that ΦRB almost doubles in the region of long distances and large radii. The enhancement for the two fused spheres can be explained by looking at Figure 7 (left) in which the ratios of Γrad and Γnonrad with respect to the values for a single-sphere NP are reported. As can be seen, the two decays are affected unevenly by the change of the shape of the

Vukovic et al. MNP. The influence on Γnonrad is almost negligible if not decreasing, whereas Γrad is increased. It is also interesting to note that enhancement of ΦRB is visible in the region of long distances and large radii, where neither A nor Γrad is at a maximum. This demonstrates that the enhancement is due to the best compromise between increased Γrad and A (larger radii) while keeping nonradiative losses at reasonable levels (longer distances). Such a compromise, that can create relative brightness enhancement for molecules at 10-20 nm from the metal particle, has also been noted in previous works.11 If we fuse a third gold to the sphere, the gain in ΦRB does not continue. By comparing Γrad and Γnonrad in the most interesting region (longer distances/larger radii region), it is clear that ΦRB decreases from 2F to 3F because Γrad decreases while Γnonrad stays more or less the same (Figure 7). A detailed explanation of this unexpected behavior of Γrad is postponed to section 3.6, but we can anticipate that the phase of the induced met mol , with respect to the molecular dipole, b µK0 , is dipole, b µK0 responsible for the effect. We finally remark that the ΦRB surfaces for the single sphere and for the fused spheres appear to be qualitatively similar, although quantitatively different: both have a minimum at small radii and small distances and a maximum for large radii and large distances, with a monotonic variation between these extremes. Second, we consider changing the number of MNPs (Figures 6 and 8). When studying distance and size effects of two metal particles, the number of independently varying arguments poses a problem in the presentation of the results. There are two distances and two radii. In order to keep 3D presentations possible, here, we present results where distances and radii are kept the same (d1 ) d2 and R1 ) R2). The study of the case with d1 * d2 is shown afterward. Because of the less effective behavior of the three-sphere case, this analysis is limited to MNPs made of one or two fused spheres. The effect on ΦRB (Figure 6) is much more dramatic than what was seen for the fused spheres. Additional separate particles in the longitudinal orientation positioned on the opposite end of the chromophore increase A and Γrad by orders of magnitude, whereas doubling the number of metal particles “only” doubles Γnonrad (Figure 8). This can be qualitatively understood in a zeroth-order model where the effects of the two spheres are assumed to be independent: Γnonrad will be the sum of the energy transfer rates from the molecule to each single metal spheres, i.e., Γnonrad,2spheres ) 2Γnonrad,1sphere, whereas Γrad (and A) depend on the coherent sum of the oscillating dipoles, mol sphere,a sphere,b 2 1sphere 2 bK0 + b µK0 + b µK0 | ≈ k|2µ bK0 | ) Γrad,2sphere ) k|µ rad,1sphere ; i.e., even within this simple model, the enhancement 4Γ of Γrad is twice that of Γnonrad. Such nonlinear effects are automatically included in calculation of µK0 by the influence and mutual interaction of apparent charges on each NP. Because of the larger increase in Γrad (and A) compared to nonrad , an increase in ΦFQY and ΦRB with respect to the singleΓ particle case is observed again. However, this time, the maximum increase is not for the region of long distances but for the region of short distances. In this region, the enhancement of ΦRB is not due to relatively small Γnonrad but to large increases in Γrad (and A). This is clearly depicted in Figure 8. The high Γrad enhancement is clearly visible at small distances and large radii, an enhancement that is not compensated by a similar increase of Γnonrad. In essence, this analysis demonstrates that changing the shape and changing the number of metal particles can lead to very different results in terms of changes in radiative and nonradiative



Figure 5. (Left) Fluorescence quantum yield and (right) relative brightness for PDI near a gold spherical NP in the longitudinal orientation.

Figure 6. ΦRB for PDI near one or two gold NPs in the longitudinal orientation.

decay rates. As a net result, ΦRB is largely enhanced when the chromophore is close to two large NPs, whereas a much smaller enhancement is obtained with a single nonspherical NP. In the latter case, the most effective setup is with both large radii and distances. In the first case, however, the shape of the NP is also important. Before moving to a different analysis in terms of the nature of the metal, it is interesting to further discuss the two-NP case. We have seen that increasing the radiative decay rate is not enough to increase the relative brightness. We have also seen that an enhancement was still possible because of the sheer increase in the magnitude of the rates by a change in the shape or number of the particles. Therefore, to observe enhancement, one can count on altering the emission or absorption processes or both. Here, we show more evidence that MNPs lead to an enhancement by altering both that decay and excitation rates and that which scenario takes place depends on both the distance from the chromophore and the size of the particle. In Figure 9,

a plot of relative brightness changes with respect to two unsymmetrical distances, for three selected radii of R ) 40, 80, and 200 Å, shows how this is achieved. As can be seen, the graphs strongly depend on the NP radii. For shorter radii (Figure 9, upper left corner), the highest ΦRB is at long distances, whereas the opposite is true for the largest radius. As discussed before, in the region of long distances, both the radiative and nonradiative rates are the lowest, and ΦRB is approaching the free-chromophore value, 1. For two MNPs, it is in the region of short distances where the real enhancement is observed as soon as the radius of the NP is large enough to allow for large Γrad (and A). Focusing now on the analysis of symmetric/asymmetric arrangements, it is of interest to point out that, even though the symmetrical arrangement of MNPs does not produce the highest Γrad and Γnonrad values, it does result in the highest ΦRB (Figure 9, R ) 80 Å). In other words, an unsymmetrical arrangement of the particles around chromophore, i.e., one particle near and


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Figure 7. Relative changes in (top) nonradiative and (bottom) radiative decay rates of PDI near an NP made of (left) two and (right) three fused spheres with respect to those for the single-sphere NP. Decay rate ratios are plotted on a logarithmic scale. Red and blue colors indicate an increase and a decrease, respectively, of the corresponding decay rate.

Figure 8. Relative changes in (top) nonradiative and (bottom) radiative decay rates of PDI between two (left) single-sphere and (right) two-fusedsphere NPs with respect to those for the single sphere. Decay rate ratios are plotted on a logarithmic scale.

one far away, produces the highest rates but the lowest efficiency and enhancement. This somewhat surprising result is a consequence of the change of the magnitudes of Γnonrad and Γrad relative to each other (from section 3.1) depending on the distances and radii of the NPs. For the optimal increase in ΦRB at the short distances, the best choice is a large NP radius (thus increasing the magnitude of Γrad the most) shown in Figure 9 (R ) 200 Å). In this arrangement, the increase in A is

maximized, so the increase in ΦRB is due to the metal’s modification of the absorption process (simultaneously Γrad is increased, so ΦFQY is increased as well). The plot for R ) 80 Å demonstrates the middle ground where both absorption and emission processes have been partially affected. 3.4. Effects of Type of Metal Particle. Here, we present a comparison between gold and silver. In Figure 10, we report the changes of Γrad and Γnonrad with respect to the distance and



Figure 9. Relative brightness with respect to distances for two single-sphere gold NPs placed on each end of longitudinally positioned PDI.

Figure 10. Logarithm of (top) radiative and (bottom) nonradiative decay rates (s-1) of PDI with distance from a silver spherical particle of varying radius in the (left) longitudinal and (right) transversal orientations.

radius of the sphere for both the longitudinal and transversal orientations for a silver NP, for comparison with those for the gold NP (Figure 3). By comparison with the analogous figures for gold, it is evident that the radiative and nonradiative decay rates present exactly the same qualitative trends as observed for gold. However, silver exhibit smaller Γnonrad rates, pointing to its capability of achieving better ΦFQY at this frequency (525 nm).

This intrinsic difference between the two metals is reflected in the relative brightness as shown in Figure 11, where ΦRB is plotted with different setups of NP(s) in the longitudinal orientation. One can notice the same effects of changing shape and number of particles discussed before for gold NPs. However, one can also notice that silver displays an enhancement for a single metal particle, whereas gold does not. The enhancement


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Figure 11. Relative brightness of different PDI-silver NP(s) in the longitudinal orientation.

is even more pronounced for two and three fused spheres. However, the higher enhancement by silver is due not to higher rates but to a relatively larger contribution of Γrad than Γnonrad to the fluorescence decay rate. Overall, silver achieves higher yields and enhancements mostly because of more efficient handling of the emission process than gold. (The underlying reasons for this are further analyzed in relation to the metal’s polarizability in section 3.6.) It has been observed experimentally that surface-enhanced fluorescence (in the sense of enhanced ΦRB) for a chromophore close to a spherical metal nanoparticle requires the chromophore to be ∼100 Å from the particle.11 This is in agreement with our finding for ΦRB, showing that, in the case of a single sphere, enhancement is possible for this range of distances. Notably, the distance of maximum enhancement does not seems to depend strongly on the particle radius, but it does depend on the nature of the metal (compare Figure 11 with the analogous Figure 5 for gold) and the shape of the metal particle (compare Ag results for monomer, dimer, and trimer). 3.5. Effects of the Solvent. The solvent in our model was assumed not to exchange energy with either the chromophore or the metal particle. As a solvent, we chose water. In Figure 12, we report the results obtained for PDI-NP (one sphere) in water for both gold and silver NPs. Having emerged as be the most interesting case, we have limited the analysis to the longitudinal orientation only and to a single single-sphere NP. As can be seen from a comparison of Figure 4 (right) and Figure 9 (left upper corner), the presence of a solvent increases the relative brightness. This is due to the solvent contribution to both A and Γrad (see eqs 4 and 5), whereas its effect on Γnonrad

is almost negligible. This shows that the solvent can be used as one of the independent factors capable of inducing enhancement of fluorescence. Finally, we compared the results for the point-dipole model with our quantum mechanical model for the system in water. The agreement between the two sets of results is similar to what was already found for molecules in vacuo (from Figure 4), and thus, we do not present it in detail. 3.6. Polarization of Metal as the Reason for the Effects. To complete our analysis of the different parameters that determine possible enhancement or quenching of the fluorescence of a chromophore near MNP(s), we discuss here possible correlations between ΦRB (through A, Γrad, and Γnonrad) and intrinsic metal properties (such as polarizability). In Figure 13, we report the dispersion of the modulus (solid line) and imaginary part (dotted line) of the metal polarizability for each of the metal particles studied. Only the diagonal component along the MNP-molecule direction (corresponding to the longest axis for anisotropic MNPs) is shown, as it is the most relevant for our setup. As our interest is to understand better the different behaviors of ΦRB due to the different shapes, as shown in Figures 5 and 6 for gold and Figure 11 for silver, only the example of the largest NP is shown (namely, R ) 200Å);31 it is, in fact, in this region that the highest enhancements are found. The imaginary part of the polarizability of the metal particle (RIm) is a direct reflection of the metal’s capability to absorb energy, which is an indication of the possibility of nonradiative energy transfer from the chromophore to the metal,32 whereas the modulus of the polarizability [|R| ) (RRe2 + RIm2)1/2] is



Figure 12. Relative brightness for PDI-NP (one sphere) in water with the longitudinal orientation: (left) Au NP, (right) Ag NP.

Figure 13. Dispersion of the modulus (solid line) and the imaginary part (dotted line) of the longitudinal-axis component of the polarizability of (left) gold and (right) silver NPs made of (red) a single sphere, (blue) two fused spheres, and (green) three fused spheres. Polarizability values are in au. In the inset, an enlargement for the single-sphere case is reported.

responsible for stimulating the radiative rate of the chromophore. The maxima in the graphs indicate a plasmon resonance. One can immediately observe two effects: the rise of the intensity and the shift of the position of the maxima. The two metals exhibit similar trends but not in the same region of frequencies; thus, the position of the absorption/emission process of the chosen chromophore does not equally affect the chromophore, resulting in different behaviors for these two metals. For the simplest NP (one sphere, 1F), the two metals have very similar |R| in the range of PDI absorption/emission processes but different RIm (with gold presenting the resonance behavior, see the inset). This is reflected in higher Γrad (and A) and Γnonrad for gold. For more elliptical-shaped particles (two and three spheres, 2F and 3F), an increase of the polarizability is found, as expected because of the increase in the NP volume, but for gold, the two- and three-sphere cases present quite different behaviors with respect to the ratio |R|/RIm. At the emission wavelength, this ratio is very close to 1 in the three-sphere case, which is reflected in a similar ratio between Γrad and Γnonrad with no (or very small) enhancement in ΦRB (see Figure 6). By contrast, for silver, |R|/RIm is always significantly greater than 1, which means a dominant radiative decay and a final net enhancement in ΦRB. The differences in the maximum ΦRB values between the 2F and the 3F particles noted in section 3.3 demonstrate that intuitive reasoning is not always valid for these systems. In fact,

one would expect that 3F would give a larger ΦRB enhancement than 2F: Radiative rates scale with the polarizability of the system, and 3F has a larger polarizability than 2F. Thus, Γrad is expected to be larger for 3F than for 2F, and enhancement of ΦRB would follow. (As remarked in section 3.3, the Γnonrad values for 2F and 3F are similar in the region of maximum ΦRB.) Examination of Figures 6 and 7 shows that this is not the case. The reason is that, for emission and absorption frequencies in proximity of the plasmon resonance (as is the case with Au), changing the number of spheres affects not only the magnitude of the dipole moment induced in the metal, but also its phase with respect to the oscillating molecular dipole. In particular, going from the 1F to 2F to 3F, the Au plasmon band passes from being slightly blue-shifted to being red-shifted with respect to the emission frequency of PDI. In the blue-shifted region, the induced dipole has a small phase mismatch with the molecular dipole, and the coherent sum of the two is effective in enhancing Γrad. In the red-shifted region, the induced dipole is oscillating close to π/2 out of phase with respect to the molecular transition dipole, and the coherent sum is smaller. Clearly, the resulting effect on Γrad is due to the delicate balance between the contrasting phase and magnitude changes of the polarizability upon increasing the number of fused spheres, and it is difficult to predict without calculations. When the chromophore emits and absorbs at frequencies that are not close to the plasmon band maximum, the prediction that ΦRB should


Vukovic et al.

Figure 14. Simultaneous plot of relative brightness and size of different PDI-Au NPs in the longitudinal orientation: NR and R denote the nonradiative and radiative decay rates, respectively, and +, 0, and - indicate an increased, unchanged, and decreased rate relative to the rate of the free chromophore. Dotted lines indicate ΦRB ) 1. Note: Colors are not comparable.

increase with increasing number of fused sphere is indeed followed, as the case for silver demonstrates. 4. Summary We have presented a working method to obtain direct insight into the influence of metal nanoparticle(s) on the photoinduced properties of a chromophore. In our case, we investigated the fluorescence of N,N′-dimethylperylene-3,4,9,10-dicarboximide (PDI) in the vicinity of gold and silver nanoparticles (NPs) in vacuo and in water. Fluorescence was characterized by its amount and efficiency. ΦFQY was used as the measurement of efficiency, whereas the amount of fluorescence was measured as the relative brightness ΦRB. A complete configurational space of PDI-MNP complexes was constructed, and correlations among Φ and Γ values were drawn. A summary of these results is shown in Figure 14. These plots, together with the more detailed discussion in the preceding sections, point to rather different conditions to achieve ΦRB enhancement in the case of a single MNP or multiple MNPs: (1) For a single MNP, ΦRB is enhanced when the molecule is relatively far from the metal surface (100-200 Å) and the radius of the particle is of comparable or greater size. As was discussed before and is apparent from Figure 14, enhancement is here obtained because the nonradiative decay channel provided by the metal is not very effective at long distances, whereas the radiative decay and the absorption are still substantially amplified because of the large polarizability of the MNP. The aspect ratio of the MNP affects the achievable ΦRB values, and the quantitative values of distances and radii where they can be obtained, but does not qualitatively affect the picture with respect to spherical MNPs. (2) For a chromophore between two MNPs, enhancement is possible at all of the studied metal-molecule distances, but ΦRB is higher at small distances. In this regime, both the nonradiative and radiative decays are large, but the radiative decay benefits from being due to the coherent sum of molecular and induced dipoles, which nonlinearly strengthens the emission and absorption, whereas the nonradiative decay results from energy transfers to the two NPs that interfere only moderately. Ultimately, the ideal configuration for PDI-MNP to both increase ΦRB and produce an enhancement in fluorescence would be that with metal nanoparticles positioned in the longitudinal orientation with the chromophore’s transition

density dipole. The chromophore would be preferably tethered between the two metal particles that are ellipsoidal in shape, no larger than a few tens of nanometers, and very close to each other. The chromophore-MNP system would benefit from a dielectric environment rather than a vacuum. As for the choice of metal, that depends on the intrinsic emission and absorption frequencies of the chromophore. For PDI, gold has a plasmon resonating right at the frequencies of the chromophore’s fluorescence; silver does not. This means that the transition density dipole of the chromophore will be affected much more by gold and will therefore generate higher increases in all three rates: excitation, radiative decay, and nonradiative decay. However, the transition density dipole moment is determined by both the real and imaginary parts of the polarizability, so it is not straightforward to predict how the rates will behave. Judging from our results, the most favorable situation is when chromophore absorption and emission are red-shifted with respect to the plasmon absorption band, as is the case for the couple PDI-Ag. However, a more extensive analysis of this point is required, including an investigation of different chromophore-metal couples. Overall, although the fundamental reason for enhancement or quenching of fluorescence by a metal nanoparticle lies in the metal response to an external electric field, a prediction of a metal’s fluorescence-enhancing ability directly from the its polarizability alone is not an intuitive task. Here, however, we have shown that relatively simple quantum mechanical calculations can indeed lead toward the choice of the best chromophoremetal pair and also suggest the setup (i.e., size, shape, position, orientation) that will give the largest enhancement. Acknowledgment. This work was supported within the EU FP6, by the ERANET project NanoSci-ERA: Nanoscience in the European research area. References and Notes (1) (a) Drexhage, K. H.; Fleck, M.; Schafer, F. P.; Sperling, W. Ber. Bunsenges. Phys. Chem. 1966, 20, 1179. (b) Drexhage, K. H.; Kuhn, H.; Schafer, F. P. Ber. Bunsenges. Phys. Chem. 1968, 72, 329. (2) Chance, R. R.; Prock, A.; Silbey, R. AdV. Chem. Phys. 1978, 37, 1. (3) (a) Fleischmann, M.; Hendra, P. J.; McQuillan, A. J. Chem. Phys. Lett. 1974, 26, 163. (b) Albrecht, M. G.; Creighton, J. A. J. Am. Chem. Soc. 1977, 99, 5215. (c) Jeanmaire, D. L.; Van Duyne, R. P. J. Electroanal. Chem. 1977, 84, 1. (d) Kneipp, K., Moskovits, M., Kneipp, H., Eds.;



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(22) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer-Verlag: Berlin, 1995. (23) (a) Persson, B. N. J.; Lang, N. D. Phys. ReV. B 1982, 26, 5409. (b) Persson, B. N. J.; Andersson, S. Phys. ReV. B 1984, 29, 4382. (24) (a) Zerner, M. C. J. Chem. Phys. 1975, 62, 2788. (b) Bacon, A. D.; Zerner, M. C. Theor. Chim. Acta 1979, 53, 21. (c) Correa de Mello, P.; Hehenberger, P.; Zerner, M. C. Int. J. Quantum Chem. 1982, 21, 251. (d) Zerner, M. C.; Limpkowitz, K. B.; Boyd, D. B. ReV. Comput. Chem. 1991, 2, 313. (25) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.01; Gaussian, Inc.: Pittsburgh, PA, 2004. (26) Euler, J. Z. Phys. 1954, 137, 318. (27) Palik, E. D. Handbook of Optical Constants of Solids: Academic Press: New York, 1985; Vol. 1, p 257. (28) Donati, F.; Pucci, A.; Cappelli, C.; Mennucci, B.; Ruggeri, G. J. Phys. Chem. B 2008, 112, 3668. (29) Dulkeith, E.; Ringler, M.; Klar, T. A.; Feldmann, J.; Javier, A. M.; Parak, W. J. Nano Lett. 2005, 5, 585. (30) Bharadwaj, P.; Novotny, L. Opt. Express 2007, 15, 14266. (31) In the quasistatic limit, the dispersion of polarizability is not affected by the particle size unless the metal dielectric permittivity is size-dependent. This is our case; see eq 7. (32) To be more precise, at short distances, several MNP multipoles intervene in the molecule-to-metal energy exchange (ref 11), whereas RIm represents only the dipole contribution, which dominates at long distances. The maximum efficiency of the metal as a energy acceptor at short distances is thus slightly red-shifted with respect to the RIm peak (ref 30). Although all multipoles are taken into account in our calculations, for a qualitative rationalization of our results, reference to RIm is enough.

JP808116Y

Fluorescence Enhancement of Chromophores Close to Metal

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