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Plasmonic Enhancement of Molecular Fluorescence near Silver Nanoparticles: Theory, Modeling, and Experiment Dmitry V. Guzatov,† Svetlana V. Vaschenko,‡,§ Vyacheslav V. Stankevich,‡ Anatoly Ya. Lunevich,∥ Yuri F. Glukhov,∥ and Sergey V. Gaponenko*,‡ †

Yanka Kupala Grodno State University, Grodno, 230023, Belarus Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk 220072, Belarus § The Chemical Department, Belarusian State University, Minsk, 220030, Belarus ∥ ELTA Ltd., Aviatsionnaya St. 19/6, Moscow, 123182, Russia ‡

ABSTRACT: Metal-enhanced fluorescence of molecular probes in plasmonic nanostructures offers highly sensitive chemical and biomedical analyses, but a comprehensive theory of the phenomenon is far from being complete. In this study, a systematic theoretical analysis is provided for overall luminescence enhancement/quenching for fluorophores near silver spherical nanoparticles. The approach accounts for local intensity enhancement, radiative and nonradiative rates modification, light polarization, molecule position, and its dipole moment orientation. Numerical modeling has been performed for fluorescein-based labels (e.g., Alexa Fluor 488) widely used in biomedical studies and development. The maximal enhancement exceeding 50 times is predicted for nanoparticle diameter 50 nm, the optimal excitation wavelength being 370 nm. For long-wave excitation, bigger particles are more efficient. The experiments with a fluorescein isothiocyanate conjugate of bovine serum albumin confirmed theoretical predictions. The results provide an extensive and promising estimate for simple and affordable silver-based nanostructures to be used in fluorescent plasmonic sensors.

1. INTRODUCTION Plasmonic enhancement of luminescence (metal-enhanced luminescence) has become an active field of research during the last decades. It has definite prospective in analytical spectroscopy, nanobiosensors, display, and light-emitting devices. It has been demonstrated for molecules, atoms, and nanocrystals (quantum dots). The proximity of a metal nanobody gives rise to an increase in local electromagnetic radiation intensity, changes the probability of spontaneous photon emission, and also promotes multiple enhancement of nonradiative relaxation of an excited state. All three effects result from local modification of the dielectric function of space upon insertion of a metal nanobody which is capable to support plasmon oscillation.1−4 Each of the three above effects alone has been examined by different authors for a number of model systems. For example, in the case of a single silver nanoparticle, the calculated local enhancement of light intensity measures about 102 times,5 in a gap between two spherical nanoparticles about 103 times,6 and in a system of three specially sized and arranged nanoparticles up to 106 times.7 Modification of spontaneous emission probability for an elementary emitter near a silver ellipsoid ranges from 10−1 to 104 times,8 and in a system of two spherical silver particles it ranges from 10−3 to 107 depending on an emitter position and its dipole moment orientation.9 Notably, © 2012 American Chemical Society

in the same system, the nonradiative transition rate in the gap between nanoparticles can rise up by 108.9 For practical application, one needs the combination to be larger than 1 of enhancing (rise up of local intensity, increase of radiative transition rate) and quenching (decrease of radiative transition probability, increase of nonradiative transition rate) factors which give the overall increase in luminescence intensity upon steady-state illumination. Therefore, calculations of every factor alone do not allow for the net enhancement/quenching of luminescence in plasmonic nanostructures to be predicted. Experiments performed by a number of groups did show luminescence enhancement from 2...3 to 30 times.10−24 Reviews of experimental activity can be found in refs 3, 4, 25, and 26. The maximal enhancement occurs for spatially organized nanostrucutres developed by means of submicrometer nanolithography, vacuum deposition, and etching.17,22,24 50-Fold enhancement was found for a spherical gold nanoshell over a dielectric nanoparticle.27 However, these approaches seem to be rather expensive and cumbersome for wide routine applications, e.g., in analytical spectroscopy or biomedical analyses. Simple and affordable techniques of luminescence enhancement will be welcome. Extensive calculations for a Received: February 17, 2012 Revised: March 30, 2012 Published: April 10, 2012 10723

dx.doi.org/10.1021/jp301598w | J. Phys. Chem. C 2012, 116, 10723−10733

The Journal of Physical Chemistry C

Article

single gold nanoparticle and a single light-emitting molecule28 and the fine experiments showed that luminescence can be enhanced by 6 to 7 times. In these calculations, for the specific excitation wavelength (650 nm) enhancement was found to occur for a gold nanoparticle diameter more than 20 nm. For practical applications of metal-enhanced luminescence, one should know the optimal nanoparticle size (and shape), the spectral features (dependence on excitation and emission wavelengths), and spatial behavior (dependence on a fluorophore position and orientation) of the overall luminescence enhancement/quenching factor. The latter should necessarily involve all the three above-mentioned factors. Though single molecule experiments are very instructive in the context of basic light−matter interaction, practical spectroscopy and optical engineering need overall intensity enhancement to occur for a statistically big number of emitters with random displacement within an ensemble of metal nanoparticles. In this paper, a systematic theoretical analysis is reported on possible luminescence enhancement for molecules (atoms, nanocrystals) near spherical silver nanoparticles of different size. Notably, dielectric substrates covered with silver nanoparticles can be routinely fabricated in a lab or in commercial production without expensive processes of nanolithography, molecular beam epitaxy, (electro)chemical etching, and vacuum deposition. The theoretical findings are confirmed in the experiments with biomolecules labeled with fluorescein isothiocyanate on silver-coated substrates.

plasmonic effect to come into play, there are three principal factors each featuring spectral and distance dependence. Moreover, the incident field enhancement factor is calculated based on classical electrodynamics, and here the mutual orientation of incident electric field and wave vector are important, whereas modification of quantum yield is essentially the quantum electrodynamics problem with the probe emitting dipole orientation and its displacement versus nanoparticle to be the major parameters. To summarize, the calculation of the overall enhancement (or quenching) breaks into the two separate problems, each depending on the specific list of parameters. 2.1. Intensity Enhancement Factor. The G factor near a spherical particle with a radius, made of a material with dielectric permittivity ε and displaced with its center located at the r = 0 point, in a general case of an arbitrary particle diameter (the Mie theory29) is expressed by rather cumbersome formulas. Nevertheless, in the case of smaller nanoparticles, i.e., particles whose size is negligibly small as compared to the light wavelength, a plane incident electromagnetic wave illuminating a particle can be approximated by a homogeneous electric field. As is known, in a homogeneous field only dipole type plasmonic resonances can be excited.2 Therefore, a spherical nanoparticle in a homogeneous field looks like a dipole with the moment2 dp = αE0, with α = a3(ε − 1)/(ε + 2) being the polarizability of the spherical particle. Then, inserting the particle dipole moment dp in the general expression for a dipole field,29 we arrive at the induced portion of the electric field near a nanoparticle in a form

2. THEORY The luminescence intensity is proportional to the absorbed light intensity and the quantum yield Q. Supposing the absorption coefficient of light by a molecule (atom, nanocrystal) in plasmonic nanostructures remains the same as in vacuum and intensity independent, the overall factor of luminescence intensity modification F for an elementary emitter in a point with r vector reads

Ep = −

γrad(ω′, r) |E(ω , r)|2 2 |E0(ω)| γrad(ω′, r) + γnonrad(ω′, r)

|E(ω , r)|2 |E0(ω)|2

(1)

Gtang

(2)

γrad(ω′, r) γrad(ω′, r) + γnonrad(ω′, r)

(d p·r)r r5

(4)

⎛ ε − 1 ⎞⎛ a ⎞ 3 ⎟⎜ ⎟ = 1−⎜ ⎝ ε + 2 ⎠⎝ r ⎠

2

2

(5)

where Gnorm corresponds to the radial orientation of the E0 field, i.e., normal to a nanoparticle surface, and G tang corresponds to the tangential orientation of the E0 field with respect to a nanoparticle surface. Equations 5 allow for calculation of electric field enhancement and light intensity enhancement near a spherical particle whose size is small as compared to the light wavelength. For bigger particles, one needs to use more general but cumbersome expressions given in the Appendix (eq A.5). To verify the applicability of eqs 5, numerical modeling has been performed for particles with size a < 5 nm, i.e., actually small as compared to light wavelength. In this case, the results based on the Mie theory and derived from eqs 5 indeed coincide, which indicates that eqs 5 are correct for smaller nanoparticles. 2.2. Modification of Spontaneous Emission Rate. The spontaneous radiative transition rate for a dot-like molecule

is the intensity enhancement factor for excitation light; and Q=

+3

⎛ ε − 1 ⎞⎛ a ⎞ 3 ⎟⎜ ⎟ Gnorm = 1 + 2⎜ ⎝ ε + 2 ⎠⎝ r ⎠

where ω (ω′) is excitation (emission) radiation frequency; E (E0) is the electric field of light wave with (without) a metal nanobody, G=

r

3

where r is the radius vector from the particle center to a point of interest where the electric field is calculated and r = |r|. The total field near a nanobody will be equal to the sum of the induced inhomogeneous field (eq 4) and the homogeneous incident field E0, i.e., E = E0 + Ep. Then G factor defined by eq 2 for a spherical particle reads

F(ω , ω′, r) = G(ω , r)Q (ω′, r) =

dp

(3)

is luminescence quantum yield in the presence of a nanobody. Here γrad (γnonrad) is the radiative (nonradiative) transition probability from the excited to the ground state of the quantum system in question. Hereinafter, the arguments ω, ω′, and r are omitted for brevity. Notably, an a priori estimation of fluorescence enhancement is not straightforward. Though a noticeable overlap of the metal nanostructure extinction spectrum with the fluorescence excitation spectrum is the primary precondition of the very 10724



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placed near a small nanoparticle (a ≪ λ, λ′) can be calculated using the formula2,30 γrad γ0

=

appears to be helpful. Namely, modification of the photon local DOS is taken to be equal to the modification of electromagnetic emission rate by a classical oscillator placed at the point of interest with respect to the rate in the vacuum. Therefore, taking de fide the conception of photon emission in the course of quantum jumps we use classical equations to calculate modification of transition rate (probability) in a system with complicated topology. In other words, while the classical electrodynamics cannot explain the very event of a photon emission in the course of atomic or molecular transition, it is capable to offer the computational technique for its rate calculation. Such a “computational” compromise in a sense dates back to the very dawn of quantum physics. In 1900, the same formula for blackbody radiation was proposed by Rayleigh based on electromagnetic modes counting (later on acquired the notion of density of states)33 and by Planck based on the energy density of a classical oscillator.34 Therefore, the identical form of eqs 5 and 9 means that the spontaneous emission rate is modified near a nanobody owing to spatial redistribution of some “probe” field at the frequency of emitted radiation. It is also possible to speak about electromagnetic vacuum mode redistribution. This approach is fully in line with our previous considerations,35 in which the so-called “hot spots” in plasmonically enhanced spectroscopy are portions of space with enhanced Q-factor simultaneously at the frequencies of incident and emitted (scattered) radiation. In the context of the above discussion on the certain “convergence” of classical and quantum approaches to calculation of probability (rate) of photon emission, it is reasonable to consider the introduction of the nanoantenna notion in nanophotonics during the last years (see, e.g., refs 16 and 36−40). A classical antenna defines conditions for electromagnetic radiation propagation emitted by a classical oscillator. In nanophotonics, an emitter (a molecule or an atom) is always a quantum system rather than a classical oscillator. Therefore, the nanoantenna-based approach should be treated as a useful computational procedure provided that we understand that photon creation in the course of a quantum system downward relaxation by no means can be derived or explained by classical radiophysical techniques. Finally, we note such a computational quantum−classical “duality” has been examined in detail in the context of light emission by a quantum versus a classical emitter in front of a mirror.41 2.3. Rate of Nonradiative Decay of an Excited State. For the nonradiative spontaneous decay rate of an excited molecule placed near a metal nanoparticle of arbitrary size, one again arrives at cumbersome expressions (see Appendix, eqs A.8 and A.9). However in the case of a smaller particle (a ≪ λ, λ′), these expressions reduce to (see ref 2)

|d 0 + δ d|2 |d 0| 2

(6)

where d0 is the molecule dipole moment in vacuum, and δd is the induced dipole moment which a nanoparticle acquires in the presence of a molecule. Using expressions for induced dipole moment of a spherical particle in a field of a dipole,8 eq 6 can be written as ⎛ ε − 1⎞ ⎟⟨E⟩ δ d = a3⎜ ⎝ε + 2⎠

(7)

with ⟨E⟩ being the field of a dipole source (molecule) averaged over the volume of a spherical particle. Calculating the averaged field in eq 7, we arrive at the general expression ⎛ ε − 1 ⎞⎡ d 0 (d ·r)r ⎤ ⎟⎢ − + 3 05 ⎥ δ d = a3⎜ 3 ⎝ ε + 2 ⎠⎣ r ⎦ r

(8)

where r is the radius vector from the particle center to the point of a molecule location, and r = |r|. Substituting eq 8 into eq 6, one can arrive at the following expressions for the radiative transition probability of a molecule located near a spherical nanoparticle2 ⎛γ ⎞ ⎛ ε − 1 ⎞⎛ a ⎞ 3 ⎟⎜ ⎟ ⎜⎜ rad ⎟⎟ = 1 + 2⎜ ⎝ ε + 2 ⎠⎝ r ⎠ ⎝ γ0 ⎠norm ⎛γ ⎞ ⎛ ε − 1 ⎞⎛ a ⎞ 3 ⎟⎜ ⎟ ⎜⎜ rad ⎟⎟ = 1−⎜ ⎝ ε + 2 ⎠⎝ r ⎠ ⎝ γ0 ⎠tang

2

2

(9)

Here the “norm” subscript indicates the radial orientation of a molecule dipole moment with respect to a spherical nanoparticle surface, whereas the “tang” subscript implies its tangential orientation with respect to a spherical nanoparticle surface. Notably, eqs 9 formally coincide with eqs 5. However their difference is to be highlighted. First, in eqs 5 the concern is the radial and tangential orientation of the real field, whereas eqs 9 deal with the spontaneous transition rate with a photon emission for molecules differing in orientation with respect to a nanoparticle surface. Second, in eqs 5 calculations should be made for incident light frequency ω (wavelength λ), whereas in eqs 9 calculations are made for the emitted light frequency ω′ (wavelength λ′). Nevertheless, such a coincidence is not fully incidental. In terms of the quantum electrodynamics, the probability of a quantum downward transition with spontaneous photon emission is proportional to the electromagnetic mode density (photon density of states, DOS).31 In a spatial structure with complicated distribution of dielectric permittivity (including plasmonic structures), modification of the spontaneous transition probability is treated as a consequence of the enhancement/depletion of the photon local DOS (see, e.g., ref 3). The latter, in turn, can be treated as development of spatial areas with enhanced (depleted) Q-factor at the frequency in question with respect to the corresponding values in vacuum values. However, the very definition of the photon local DOS meets known methodological problems.3 Here the reasonable and meaningful operational approach by D’Aguano et al.32

⎛γ ⎞ 3 ⎜⎜ nonrad ⎟⎟ = 2(k 0r )3 ⎝ γ0 ⎠norm

⎞ ⎛ ⎞ 2n + 1 ⎛ ε−1 Im⎜ ⎟ r ⎝ ε + (n + 1)/n ⎠

∞

∑ (n + 1)2 ⎜⎝ a ⎟⎠ n=1

⎛γ ⎞ 3 ⎜⎜ nonrad ⎟⎟ = 3 γ 4( k ⎝ 0 ⎠tang 0r ) ⎛a⎞ ⎟ ⎝r ⎠

⎜

∞

∑ n(n + 1) n=1

⎛ ⎞ ε−1 Im⎜ ⎟ ⎝ ε + (n + 1)/n ⎠

2n + 1

(10) 10725



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where k0 is the wavenumber (in vacuum) at the frequency ω′, and the subscript “norm” (“tang”) means normal (tangential) orientation of a molecule dipole moment with respect to a nanoparticle surface. From eqs 10, one can see that the rows in these expressions diverge when a molecule is approaching a nanoparticle (r → a). This means the nonradiative spontaneous decay rate tends to infinity. Therefore, the quantum yield in this case will tend to zero. In other words, luminescence quenching will occur. In this case, an excited molecule energy converts into heat by means of Joule losses. Contrary to the above case, the nonradiative decay rate tends to zero when the imaginary part of the particle dielectric function equals zero as is seen from eqs 10. In other words, since in pure dielectrics no electric current can be initiated, then no luminescence quenching can occur. The luminescence quenching brings about serious difficulties in elaboration of light-emitting nanodevices using metal nanosctructures. Therefore, searching for optimal configuration of nanoparticles, of their shape, as well as optimal emitter− nanoparticle distance to minimize the quenching factor while keeping the other factors high, does represent a challenging problem in nanoplasmonics.

3. NUMERICAL MODELING The analytical expressions derived in Section 2 point at the true factors influencing and defining luminescence enhancement. However, the homogeneous field approximation which is valid for very small nanoparticles (about or below 5 nm) gives the wrong excitation spectrum data upon increase of a particle size to 20−100 nm. This happens since the simple approximation does not account for the growing scattering cross-section in the long-wave spectral range with respect to the intrinsic plasmon resonance (about 350 nm for silver). In this section, the results of numerical modeling are presented without an assumption on extremely small metal nanoparticle size. The computation technique is described in detail in the Appendix. All calculations were done for silver spherical particles with respect to the emission wavelength 530 nm which corresponds to the emission maximum of fluorescein molecules and its derivatives (e.g., fluorescein isothiocyanate and Alexa Fluor 488) that are widely used as fluorescent labels in biospectroscopy and routine medical practice. To the best of our knowledge, this is the first extensive numerical analysis for silver nanoparticles in the context of fluorescence sensing with the all-acting factors taken into account. In calculations, a molecule is assumed to have a dipole moment oriented normally to a spherical silver particle surface, and that incident light has the electric field E along the molecule dipole moment (insets in Figure 1). This configuration gives the maximal enhancement factor. The dielectric permittivity spectrum for silver was taken from ref 42. Figure 1 shows the luminescence enhancement factor F, the intensity enhancement factor G, and the quantum yield Q versus molecule−nanoparticle distance Δr for the two values of nanoparticle diameter, 20 and 50 nm. The excitation wavelength is 410 nm. One can see that the luminescence enhancement factor for a 20 nm particle only slightly exceeds 1 in the range of distances from 4 nm onward. For a 50 nm particle, enhancement readily develops starting from the distance about 1 nm onward until at least 30 nm, the maximal F value being about 8. For a nanoparticle diameter of 50 nm,

Figure 1. Dependencies of the incident intensity modification factor G, quantum yield Q, and the total luminescence intensity factor F on a molecule distance Δr to a silver nanoparticle surface with diameter (a) 20 nm and (b) 50 nm. The excitation wavelength is 410 nm, and the emission wavelength is 530 nm. The molecule dipole moment is normal to a silver particle surface and is parallel to the electric field E of the excitation light.

enhancement occurs for distances of 1−30 nm, the maximal value of enhancement factor being about 10. Figure 2 represents F(Δr) dependencies for the same emission (530 nm) and excitation (410 nm) wavelengths. One can see that an increase in a particle size results in a steady increase in the enhancement factor. Note that choosing of the optimal set (molecule−metal spacing, excitation wavelength, particle size) of values for the specific emission wavelength is a complicated and multiple parameter task. The simple curves like those in Figures 1 and 2 do not allow for optimization to be made. Moreover, the existence of the hidden factors may result in the wrong choice under conditions of insufficient theoretical analysis of the problem. For example, when looking at Figure 2, one may suppose that the bigger particles always offer higher enhancement factor. However, this is valid for the long-wave portion of excitation wavelength with respect to the intrinsic plasmon resonance (350 nm). Figure 3 shows that an increase in size does not simply rise up enhancement factor F but instead shifts to the red the whole F(λ) spectrum. This shift comes from the growing contribution of the scattering component to a particle extinction spectrum when its size is not negligible as compared to the excitation wavelength (see, e.g., refs 3 and 5 for details). The maximal absolute value of enhancement factor exceeds 50 10726



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The size of silver nanoparticles can be controlled by various chemical synthesis techniques.43−45 The distance between a molecular luminophore and a silver film with high accuracy can be controlled by layer-by-layer electrostatic deposition based on sequential electrostatic self-assembly from solutions of oppositely charged substances, typically polyelectrolyte macromolecules.46 We used positively charged polycation polydiallyldimethylammonium chloride (PDADMAC, M = 200 000 g/M, Aldrich) and negatively charged polyanion sodium polystyrene sulfonate (PSS, M = 70 000 g/M, Aldrich).14,47 The conjugate of bovine serum albumin (BSA) with fluorescein isothiocyanate (FITC) has been chosen as luminophore (Fluka). 4.1. Film Preparation Technique. Glass substrates of 1 × 2 cm2 size were cleaned by means of ultrasonic treatment in isopropanol and then kept in a mixture of H2O−H2O2−NH3 (1:1:1) at 70 °C for 15 min. After washing in water, substrates were covered with a polycation layer (PDADMAC, 1 g/L in 0.5 M NaCl) during 20 min to develop positive charge on a glass surface. Silver sol was synthesized by the AgNO3 citrate reduction technique.48,49 The negative charge of silver particles in sol resulting from ion citrate adsorption allows for their electrostatic deposition on PDADMAC-modified substrates. Deposition has been performed by dipping of half of a substrate surface in a silver sol for 24 h. The silver-free remaining portion of the substrate served as a reference sample. To develop a dielectric spacer, the whole substrate surface was covered by alternate PDADMAC and PSS layers (totally 1, 3, 5, or 7 layers) according to the procedure that has been described elsewhere,14,47 a PDADMAC layer being the last one in every sample. BSA-FITC was applied on a PDADMAC layer by soaking in 3.7 × 10−6 M aqueous solution during 1 h. 4.2. Measurements. Transmission electron microscopy (TEM) was performed using a S-806TEM/SEM (“Hitachi”, Japan). Atomic force microscope (AFM) images of silver films were taken in air using a Ntegra Prima AFM/STM microscope (“NT-MDT”, Russia). Optical density spectra were measured in the 20−800 nm range with a Cary-500 spectrophotometer (Varian, USA). Luminescence spectra were registered with a grating spectrograph S3801 (Solar TII, Belarus) combined with a liquid nitrogen cooled silicon CCD camera (Princeton Instruments, USA). Luminescence excitation was performed with a cheap and affordable commercial light-emitting diode with the emission spectrum peaking at 460 nm. All optical measurements were made at room temperature (∼300 K). Emission spectra have not been corrected for spectral response of the detecting system since the goal of all measurements was reduced to plasmonic enhancement evaluation rather than spectral shaping analysis. 4.3. Results. The SEM image of silver nanoparticles in sol (Figure 6a) shows the mean diameter to be 2a = 42 nm with normal dispersion σ = 25 nm (145 particles were used for this estimate). AFM data in Figure 6b show the substrate covered with silver sol over a PDADMAC-modified surface. At first glance, nanoparticles after deposition on a substrate look somewhat bigger. However, the careful analysis of 177 single particles in the AFM image which are not superimposed over another particle(s) have led to nearly the same result as SEM image analysis. Namely, we found 2a = 47 nm with normal dispersion σ = 31 nm. The optical density spectrum of a substrate containing silver nanoparticles and BSA-FITC features a maximum near 430 nm

Figure 2. Dependencies of the luminescence intensity factor F on a molecule distance Δr to a silver nanoparticle surface with diameter 20, 50, and 80 nm (from bottom to the top). The excitation wavelength is 410 nm, and the emission wavelength is 530 nm. The molecule dipole moment is normal to a silver particle surface and is parallel to the electric field E of the excitation light.

Figure 3. Dependencies of the luminescence intensity factor F on the excitation wavelength for silver nanoparticle diameter 20, 50, and 80 nm. The emission wavelength is 530 nm. The molecule dipole moment is normal to a silver particle surface and is parallel to the electric field E of the excitation light. A molecule distance to a silver nanoparticle surface Δr = 6 nm.

and occurs for 50 nm particle and 370 nm excitation wavelength. Instead of single-argument functions like those in Figures 1−3, mapping of the enhancement factor versus two rather than one argument is much more instructive and useful. Figure 4 shows the F dependencies versus excitation wavelength and a molecule position. The emission wavelength is 530 nm throughout, whereas a silver particle diameter discretely ranges from 20 to 150 nm. Interestingly, the optimal distance both for the case of gold28 and for the case of silver appears to be the same, about 6 nm. The maximal value of the luminescence enhancement factor FMAX in calculations was found for nanoparticle diameter 50 nm (Figure 5) and occurs for an excitation wavelength of about 360 nm in the range of molecule−particle distance of about 5−7 nm.

4. EXPERIMENT It has been shown in Sections 2 and 3 that silver nanoparticle size and molecule−nanoparticle distance are the key parameters in synthesis of nanostructures with enhanced luminescence. 10727



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Figure 4. Calculated total luminescence enhancement factor F for the emission wavelength λ′ = 530 nm as a function of excitation wavelength λ and the distance (Δr = r − a) of a molecule from a silver nanoparticle surface for a number of nanoparticle diameter 2a values from 20 to 140 nm. The latter is indicated on top of every graph. A molecule dipole moment is oriented normal to the nanoparticle surface and parallel to the incident light electric field E.

(Figure 7). Since the excitation maximum (460 nm) is close to the film extinction maximum defined by the surface plasmon resonance, one may expect BSA-FITC fluorescence enhance-

ment at a certain distance from the silver surface. Table 1 summarizes experimentally obtained values of BSA-FITC fluorescence enhancement with silver film as compared to the 10728



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Figure 5. Calculated maximal values of luminescence enhancement factor FMAX versus silver nanoparticle diameter for an optimized combination of excitation wavelength and molecule−nanoparticle distance. Emission wavelength is 530 nm everywhere.

Figure 7. Optical density spectrum of a sample containing three layers of polyelectrolytes + silver + BSA-FITC conjugates on a glass substrate. The arrow indicates the emission maximum position of the LED used for luminescence excitation.

reference sample depending on the number of layers in a polyelectrolyte spacer with its thickness indicated. According to ref 50, for PDADMAC/PSS alternating layers, one layer thickness equals 1.4 nm, and then the total thickness for

Table 1. Enhancement Factors Found for Samples with Different Spacers number of polyelectrolyte layers

spacer thickness50 (nm)

photoluminescence enhancement IAg/Iglass

1 3 5 7

1,4 3,3 6,6 8,5

5,1 5,4 2,8 3,1

multiple layers appears to be lower than the simple product of 1.4 nm and layer number. Therefore, in accordance with ref 50, the spacer thickness is supposed to range from 1.4 to 8.5 nm. The biggest luminescence enhancement was observed for the sample containing three polyelectrolyte layers (thickness is 3.3 nm). Figure 8 shows the emission spectrum of this sample along with the reference one taken from the silver-free portion of the same substrate.

Figure 8. Luminescence emission spectrum of a BSA-FITC conjugate on a sample containing three polyelectrolyte layers on a pure glass substrate (dashed line) and on a glass substrate covered with silver (solid line).

Data in Figure 8 were obtained with unpolarized excitation light. When linearly polarized light was used for luminescence excitation, the enhancement factor was found to vary from 7.1 (the E vector is parallel to the plane of incidence) to 4.8 (the E vector is normal to the plane of incidence). Such anisotropy of the luminescence enhancement factor may be indicative of dominating molecule orientation normally with respect to a

Figure 6. (a) TEM image of silver nanoparticles in sol. (b) AFM image of a glass substrate covered with silver nanoparticles. 10729



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Since the field enhancement factor G near a spherical particle depends on orientation of the radius vector r (from a particle center to a molecule position), it is reasonable to make further averaging over r to compare experimental findings with the theoretical predictions. If intermolecular and interparticle effects are ignored, the case of a big number of molecules can be reduced to the case of a single molecule and a single nanoparticle. However, different locations and orientations of molecules will correspond to different field enhancement factor G values. Moreover, for bigger particles spatial field distribution becomes complicated,5 and averaging is necessary for the effect to be accounted accurately. To calculate F factor with averaging, we use the following expression (see eqs A.7 and A.10 in the Appendix)

substrate surface. However, going beyond single-nanoparticle consideration, we cannot exclude that p-polarization promotes development of surface plasmon polaritons along the nanotextured surface. Note, the observed enhancement factors are close to those reported for fluorescein-labeled oligonucleotides capped on silver nanoparticles51 as well as BSA-FITC on a deposited and annealed silver island film.47 Experimental data are to be compared with the calculated ones. However, to apply the modeling results presented in Section 3 one needs to account for (i) size distribution of silver nanoparticles and (ii) random molecule orientation and position with respect to a closest nanoparticle. We found that accounting for the finite size distribution (Figure 9) gives the

⟨Fnorm(ω , ω′, r)⟩ = ⟨G(ω , r)⟩Q norm(ω′, r)

(11)

Here the molecule orientation is implied to be random but normal with respect to the particle surface. Molecules are therefore treated as “hedgehog’s needles” illuminated by linearly polarized light. The results of enhancement factor calculations with averaging both over orientation and over size distribution are shown in Figure 10. Note, this doubleaveraging, though being seemingly more adequate to the experimental conditions, gives lower enhancement factors as compared to the observed ones. The possible reason for such a discrepancy can be related to the actually existing alignment of fluorescent labels. This is supported by the observed anisotropy of fluorescence enhancement. When linearly polarized light is applied for excitation, experimental enhancement rises up by about 20% for the E vector oriented within the plane of incidence (p-polarized light) and falls down by about 20% for the E vector oriented normally to the plane of incidence (s-polarized light). Note that the experimental conditions (an ensemble of molecules versus an ensemble of nanoparticles) are much more complicated than the simple “one-molecule−one-particle” model, even provided the averaging over particle sizes and molecule orientations is made. We cannot exclude the contribution to both extinction and fluorescence enhancement from nonspherical particles as well as enhancement from coupled nanoparticles (plasmonic “dimers”) for which enhancement may strongly differ from the single particle case. Experimental results may also be influenced by the wide (Δλ = 25 nm at half-maximum) spectrum of the excitation source (LED) in a sense that the enhancement is in fact the integral over the emission spectrum of the LED. For possible practical applications of silver-based substrates in routine analytical (bio)spectroscopy, it is important that the experiments did not reveal (in accordance with the theory) sharp dependence of luminescence enhancement on the molecule−silver spacing d in the range d = 1.4−8.5 nm (Table 1).

Figure 9. Calculated weighted total factor of luminescence intensity enhancement F for emission wavelength λ′ = 530 nm, the mean silver nanoparticle diameter 2a = 47 nm, and normal dispersion σ = 31 nm. (a) F dependence on excitation wavelength and molecule−nanoparticle distance. (b) F dependence on excitation wavelength λ for molecule−nanoparticle distance Δr = r − a = 6 nm. Molecule dipole moments are oriented normal to the nanoparticle surface and parallel to the incident light electric field E.

overall enhancement factor close to or somewhat lower than that observed in the experiments. Data in Figure 9 were calculated based on particle normal size distribution for the given parameters with a 10 nm step along the size distribution function in the range from 10 to 100 nm. Since orientation nonaveraged calculations correspond to an experimental situation with linearly polarized light and aligned molecules, the experimentally observed 7.1-fold enhancement versus 6-fold calculated for excitation wavelength 460 nm can be interpreted as rather reasonable agreement of the theory and experiment.

5. CONCLUSION A straightforward theoretical model is proposed for modeling of luminescence enhancement/quenching for fluorophores near silver spherical nanoparticles. The approach takes into account local intensity enhancement, radiative and nonradiative rates modification, light polarization, molecule position, and its dipole moment orientation. Numerical modeling has been developed with size-dependent extinction contribution for larger metal particles and averaging over molecule orientation. 10730



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incident light frequency ω as the argument, whereas the quantum yield Q should acquire the ω′ argument, i.e., frequency of the emitted radiation. Therefore, the emitted frequency should be used when calculating Q, namely, in the wavenumber and in the dielectric function.42 To calculate field enhancement factor G, consider a spherical particle upon illumination by a plane linearly polarized electromagnetic (EM) wave. Let the wave propagate in the positive direction along the z axis, the polarization being aligned along the x axis. The center of the particle is located at the origin of the coordinate system. The ambient medium is vacuum. The problem solution for electromagnetic wave scattering by a sphere is well-known and is described by the Mie theory.52 The electric field of incident EM wave can be written as29 E0(ω , r) = E0eik 0z − iωt ex ∞

= −E0e−iωt ∑ i n n=1

2n + 1 (0) (m(0) o1n − i ne1n) n(n + 1)

(A.1)

where E0 is the incident wave amplitude; k0 = ω/c is the wavenumber; ω is incident wave frequency; c is the speed of light in vacuum; ex is the unit vector along the Cartesian x axis; 29 (0) and m(0) o1n and ne1n are the spherical vectorial functions m(0) o1n =

Figure 10. Calculated total factor of luminescence intensity enhancement F for emission wavelength λ′ = 530 nm, mean silver nanoparticle diameter 2a = 47 nm, and normal dispersion σ = 31 nm with averaged field enhancement factor G over molecule orientation with respect to incident field vector E. (a) F dependence on excitation wavelength and molecule−nanoparticle distance. (b) F dependence on excitation wavelength λ for molecule−nanoparticle distance Δr = r − a = 6 nm. Normal orientation of the molecule with respect to nanoparticle surface is implied.

ψn(k 0r ) ⎛ Pn1(cos θ ) ⎜eθ cos φ k 0r ⎝ sin θ ⎞ ∂P1(cos θ ) − eφ n sin φ⎟ , ∂θ ⎠

n(0) e1n = er n(n + 1) +

ψn(k 0r ) (k 0r )2

Pn1(cos θ )cos φ

⎞ ψn′(k 0r ) ⎛ ∂Pn1(cos θ ) P1(cos θ ) ⎜eθ cos φ − eφ n sin φ⎟ ∂θ sin θ k 0r ⎝ ⎠ (A.2)

A computational experiment is described for the specific emission wavelength 530 nm corresponding to fluoresceinbased labels (e.g., Alexa Fluor 488) widely used in biomedical studies and developments. The maximal enhancement exceeding 50 times is predicted for nanoparticle diameter 50 nm and excitation wavelength 370 nm. For longer excitation wavelengths, bigger particles are more efficient. The experiments with fluorescein isothiocyanate labeled bovine serum albumin on top of silver nanoparticles with the mean diameter about 50 nm confirmed the principal theoretical predictions. For linearly polarized (p-polarization) LED excitation light (460 nm), more than 7-fold enhancement has been readily observed with no sharp dependence of enhancement factor upon molecule−silver distance.

where er, eθ, and eφ are unit vectors of the spherical coordinate system;29 r = |r| is the length of the radius vector from the particle center to a point of interest; 0 ≤ θ ≤ π and 0 ≤ φ ≤ 2π are spherical angles, the function ψ n (k 0 r) = (πk 0 r/ 2)1/2Jn+1/2(k0r) with Jn+1/2(k0r) being the Bessel function;53 P1n (cos θ) is the associated Legendre function;53 and prime means the function derivative with respect to its argument. The electric field which is induced near a particle in the EM wave field (eq A.1) can be written as29

APPENDIX Here the explicit formulas used in calculations are derived for the luminescence intensity enhancement factor F = GQ for a molecule near a metal spherical particle. For brevity, the general expressions for the G factor (incident field enhancement) and for quantum yield Q are written with the same argument ω (frequency), though in the final formulas G should have

(1) where m(1) oln and neln are the spherical vectorial functions whose (0) form can be obtained from eq A.2 for vectors m(0) oln and neln , respectively, when substituting the function ψn(k0r) and its derivative by the ζn(k0r) function and its derivative, with ζn(k0r) (1) = (πk0r/2)1/2H(1) n+1/2(k0r) and Hn+1/2(k0r) being the Hankel 53 function of the first kind. The Mie coefficients entering eq A.3 read

∞

Ep(ω , r) = −E0e−iωt ∑ i n n=1

2n + 1 (1) (an m(1) o1n − ibn ne1n) n(n + 1) (A.3)

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10731


The Journal of Physical Chemistry C an = − bn = −

Article

ψn(k 0a ε )ψn′(k 0a) −

ε ψn′(k 0a ε )ψn(k 0a)

ψn(k 0a ε )ζn′(k 0a) −

ε ψn′(k 0a ε )ζn(k 0a)

where γ0 is the radiative decay rate in a free space (i.e., without a spherical particle); r = |r| is the length of radius vector plotted from a particle center to the molecule position; the “norm” subscript indicates the case when the molecule dipole moment is normal to a particle surface; and subscript “tang” indicates the case of tangential orientation of the molecule dipole moment with respect to a particle surface. For the nonradiative decay rate, the straightforward analytical expressions can also be derived. However, it is more convenient to find out the full rate of spontaneous decay γtot, which is the sum of the radiative and nonradiative rates. The full decay rate reads2

ε ψn(k 0a ε )ψn′(k 0a) − ψn′(k 0a ε )ψn(k 0a) ε ψn(k 0a ε )ζn′(k 0a) − ψn′(k 0a ε )ζn(k 0a) (A.4)

where a is the metal particle radius and ε is its dielectric permittivity (depending on ω). To calculate field enhancement factor G at some point r near the particle under consideration, one needs to calculate for this point the value G(ω , r) = =

⎛ γ (ω , r) ⎞ 3 ⎜⎜ tot ⎟⎟ =1+ 4 γ 2( k ⎝ ⎠norm 0r ) 0

|E0(ω , r) + Ep(ω , r)|2 |E0(ω , r)|2

n=1 2 Re{bnζn (k 0r )}

|E0(ω , r) + Ep(ω , r)|2 |E0|2

⎛ γ (ω , r) ⎞ 3 ⎜⎜ tot =1+ ⎟⎟ γ0 4(k 0r )2 ⎝ ⎠tang

(A.5)

where E = E0 + Ep is the full electric field near the particle. To calculated averaged G factor, one need to average eq A.5 over all possible directions of radius vector r, i.e., over spherical angles θ and φ. Then the averaged factor will read ⟨G(ω , r)⟩ =

1 4π |E0|2

∫0

2π

∫0

∞

∑ (2n + 1)Re{anζn2(k 0r) n=1

+ bn(ζn′(k 0r ))2 }

π

dθ sin θ

(A.9)

dφ |E0(ω , r) + Ep(ω , r)|2

where γ0 and subscripts “norm” and “tang” have the same meaning as in eqs A.8. The nonradiative component of the decay rate, γnonrad, can then be calculated from eqs A.8 and A.9 as γnonrad = γtot − γrad. Quantum yield Q can be calculated using the formulas

(A.6)

After calculating integrals in eq A.6, we arrive at the expression, 1 ⟨G(ω , r)⟩ = 2(k 0r )4

∞

∑ n(n + 1)(2n + 1)

⎛ γ (ω′, r) ⎞ ⎟⎟ Q norm(ω′, r) = ⎜⎜ rad γ0 ⎝ ⎠norm

∞

∑ n(n + 1)(2n + 1) n=1

|ψn(k 0r ) + bnζn(k 0r )|2 +

1 2(k 0r )2

⎛ γ (ω′, r) ⎞ Q tang(ω′, r) = ⎜⎜ rad ⎟⎟ γ0 ⎝ ⎠tang

∞

∑ (2n + 1)(|ψn(k 0r) + anζn(k 0r)|2

where ω′ is the frequency of emitted light. Finally, the luminescence intensity factor F can be calculated as

(A.7)

To get quantum yield Q, one needs to calculate radiative and nonradiative components of a molecule decay rate near a metal nanoparticle. Decay rates can be computed both based on quantum electrodynamics and within classical electrodynamics.54,55 For radiative spontaneous decay rate γrad, one can obtain the following expressions2

Fnorm(ω , ω′, r) = G(ω , r)Q norm(ω′, r) Ftang(ω , ω′, r) = G(ω , r)Q tang(ω′, r)

(A.11)

In the quasistatic limit (k0a → 0), eq 4 can be derived from eq A.3; eq 5 can be derived from eq A.5, and eqs 9 and 10 can be derived from eqs A.8 and A.9. This confirms that all derived expressions are correct.

⎛ γ (ω , r) ⎞ ⎜⎜ rad ⎟⎟ γ0 ⎝ ⎠norm ∞ 3 ∑ n(n + 1)(2n + 1) = 2(k 0r )4 n = 1 |ψn(k 0r ) + bnζn(k 0r )|2 ⎛ γ (ω , r) ⎞ 3 ⎜⎜ rad = ⎟⎟ γ0 4(k 0r )2 ⎝ ⎠tang

⎛ γ (ω′, r) ⎞ ⎜⎜ tot ⎟⎟ γ0 ⎝ ⎠tang (A.10)

n=1

+ |ψn′(k 0r ) + bnζn′(k 0r )|2 )

⎛ γ (ω′, r) ⎞ ⎜⎜ tot ⎟⎟ γ0 ⎝ ⎠norm

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AUTHOR INFORMATION

Corresponding Author

*Phone: +375-172-840448. Fax: +375-172-840879. E-mail: s. [email protected]. Notes

∞

The authors declare no competing financial interest.

∑ n(n + 1)(2n + 1)×

■

n=1

ACKNOWLEDGMENTS The authors acknowledge assistance by Dmitry Plyakin and Iosif Sveklo in atomic force microscopy. Helpful discussions with and comments by Natalia Strekal are acknowledged. The

(|ψn(k 0r ) + anζn(k 0r )|2 + |ψn′(k 0r ) + bnζn′(k 0r )|2 ) (A.8) 10732



Article

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authors also acknowledge useful advice on sample preparation and critical comments on the manuscript by Olga Kulakovich as well as stimulating discussions with Mikhail Artemyev on polyelectrolyte chemistry. The work has been supported by the National Program “Convergence” and by the “ELTA Ltd” (Russia).

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