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Metal-enhanced Luminescence in Colloidal Solutions of CdSe and Metal Nanoparticles: Investigation of Density Dependence and Optical Band Overlap Christian Rohner,a Isabella Tavernaro,a Limei Chen,b Peter J. Klarb and Sabine Schlecht*a 5
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Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX DOI: 10.1039/b000000x The photoluminescence (PL) of semiconductor nanoparticles (SNP) is strongly modified when the semiconductor is in the proximity of a metal surface or a metal nanoparticle (MNP). The effect may be due to two different phenomena that are a) (Förster) resonant energy transfer ((F)RET) between semiconductor and metal and b) the enhanced electric field around metallic structures that arises from surface plasmon oscillations. Here we present experimental evidence of enhancement and quenching of the PL of dilute SNP colloidal solutions depending on the amount of admixed MNP and the position of the MNP plasmon band with respect to the excitation wavelength and the optical bands in the SNP. The average distance between an MNP and its next neighbor MNP is varied between ~0.1 and 2 µm by varying the MNP concentration, whereas those between MNP and SNP as well as between SNP and SNP are kept at about 0.1 µm. A model function based on the rate equations of the system is developed that yields a satisfactory description of the measured data by considering solely FRET between the particle species. The derived function is an extension to the Stern-Volmer equation, as it not only accounts for the energy transfer from the fluorescent SNPs to the MNPs, but also for the transfer of excitation from MNPs to SNPs and between MNPs. This theory provides a deeper insight into the mechanisms of metalenhanced fluorescence and fluorescence quenching phenomena.
Introduction
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The investigation of the optical properties of nanostructured materials is one of the fastest growing fields in science. In addition to their high surface to volume ratio, nanostructures exhibit phenomena which arise due to the tunable optical and electronic properties as a function of size and shape on the nanoscale. For example, metal nanoparticles (MNP) with diameters of 2-200 nm show a strong absorption and scattering of light in the visible range of the spectrum due to localized surface plasmon resonances (LSPR),1,2 and in semiconductor nanoparticles (SNP) the bandgap energy scales approximately inversely with the diameter squared of the particle due to quantum confinement effects, so that small particles of materials with bulk band gap energies in the infrared may show photoluminescence (PL) in the visible region of the spectrum.3–6 Thus, these materials' properties can be tuned to serve certain applications such as improving light harvesting in solar energy conversion,7,8 photocatalysis,9–11 bioanalytic spectroscopy12–14 and others. Recent publications show that there is an interaction between plasmonic structures and fluorophores that can lead to a quenching of the photoluminescence (PL) or to an enhancement of the intensity of the emitted light.15–19 It was found that the spatial distance between plasmonic structure and fluorophore and This journal is © The Royal Society of Chemistry [year]
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the energetic position of the plasmon resonance relative to the absorption and emission band maxima of the fluorophore play an important role.20–25 As of now, there are only few reports on PL enhancement or quenching being measured in solution, which provides a facile way to control the mean particle distance by a change of the particle concentration.21,26–29 In their recent work Li et al.26 describe concentration dependent PL enhancement of directly mixed, negatively charged CdTe NPs and negatively charged Au NPs in water, whereas the group of Lakowicz28 found only quenching of intensity when they mixed oppositely charged particles of the same two materials. In the former case the particles repulse each other and are therefore well separated, while in the latter SNPs and Au NPs form aggregates by electrostatic attraction. This indicates that there is a threshold distance as the separation of the particle species is reduced where the quenching of intensity becomes stronger than PL enhancement. In 2011 Li et al.21 reported metal-enhanced fluorescence of CdSe/ZnS core/shell particles conjugated with Au NPs by DNA oligonucleotide bridges in water with potential application in DNA detection. The distance between the particles could be controlled accurately over a range of a few nm by the number of bases in the oligonucleotide. A maximum enhancement was found when the distance between the particles was 11.9 nm, with
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a quenching of the fluorescence at shorter distance and almost no change in emission at larger distances up to 18.7 nm. The SNP with an emission maximum at 531 nm were excited at 420 nm and could in turn resonantly excite the AuNP LSPR which produced an enhanced local electric field around the Au particle. The result is explained by resonance energy transfer (RET) from SNP to Au NP at short distance and an enhanced intensity at intermediate distance by interaction of the enhanced local electric field with the SNPs. For even larger separation no interaction was found because the QDs could not excite the Au NPs plasmon resonantly and no RET from SNP to Au NP takes place. This leaves the open question whether there will be an enhancement at larger distances when the AuNP plasmon is resonantly excited by the excitation light. In order to further investigate these phenomena, we used dilute colloidal solutions containing SNPs as the fluorophore and metallic nanoparticles which show a distinct LSPR and measured the PL of the particle mixtures. As luminescent species CdSe NPs of different sizes and capped with trioctylphosphine, trioctylphosphine oxide, 1hexadecylamine and oleic acid (TOP/TOPO/HDA/Ol) were used and dodecanethiol-capped AuNP and oleic acid-capped AgNP were chosen as the plasmonic structures. The optical properties of the particles used can be adjusted by varying their size. This allows one to tune the overlap of the plasmon resonance band of the MNP and the absorption and emission band of the SNP and to investigate the influence of this overlap on the PL behavior.
Synthesis of 7 nm CdSe-NP capped TOP/TOPO/HDA/oleic acid (7 nm CdSeOl):
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All particles were synthesized according to well known procedures or slightly modified literature methods using standard Schlenk technique.30–32 Synthesis of 5 nm CdSe-NP capped TOP/TOPO/hexadecylamine (5 nm CdSeHDA):
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24.8 mg of AuPPh3Cl and 25 µL of DT were dissolved in 4 ml of benzene. 43.5 mg of tert-butylamine borane was added in one portion and the mixture was stirred at 55 °C for 1 h. The particles were then precipitated by addition of 25 ml of ethanol and purified as described above using ethanol instead of methanol to give ~1 ml of a 1 µM solution of 5 nm AuDT in 5 wt% TOPO/Dodecane.
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Synthesis of 4 nm AgNP capped with oleic acid:
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51.6 mg of 1,2-hexadecanediol were dissolved in 4 ml of 4-tertbutyltoluene at 120 °C under Ar atmosphere. A second solution of 22.1 mg of trifluoroacetate silver(I) salt and 320 µL oleic acid in 1 ml of 4-tert-butyltoluene was then injected into the first solution at 120 °C and stirred for 5 min. The mixture was allowed to cool to 60 °C and then 30 ml of ethanol were added to precipitate the particles. The product was purified as described above to give a 1 µM solution of AgNP in 5 wt% TOPO/dodecane.
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Preparation of particle mixtures for PL-measurements:
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5 g of TOPO and 3 g of HDA were mixed under argon atmosphere and the mixture was degassed at 120 °C for 30 min. The solution was then heated to 270 °C and a solution of 57.5 mg Cd(OAc)2 in 1.5 ml TOP was injected. The heating was removed and immediately after, a solution of 94.9 mg Se powder in 1.3 ml TOP was injected. After the temperature dropped to 180 °C the heating was reinstalled and the mixture was heated to 210 °C for 10 min. Then it was allowed to cool to 100 °C and diluted with 12 ml of dry toluene. Subsequently the particles were collected by precipitation with methanol and purification by a redispersion/centrifugation process using a hexane/methanol mixture. The product was dispersed in hexane, centrifuged again and separated from minor amounts of insoluble residue. A small sample was taken at that moment for TEM and UV-VIS analysis. The hexane solution is then dried under Argon flow and the particles were weighed. The diameter of the particles was determined from the TEM results and assuming a complete capping of the particles with no unbound ligand in the product the molar amount of particles was calculated. Finally the product was dissolved in an appropriate amount of 5 wt% TOPO/dodecane solution to give a 1 µM solution of the particles that was kept under air in a refrigerator until further use. The product is stable and shows PL for months.
51.4 mg of CdO, 1.15 mg of TOPO, 2.85 mg of HDA and 250 µL of oleic acid were mixed and the mixture was pumped at 120 °C for 30 min and the system flushed with argon. Then the clear solution was heated to 270 °C and a solution of 39.5 mg Se powder in 2.5 ml TOP was injected and the mixture heated for another 30 min. The product was then purified and a solution of predetermined concentration was prepared as described for 5 nm CdSeHDA. Synthesis of 5 nm AuNP capped with dodecanethiol:
Experimental section 30
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0.1 µM, 0.01 µM and 0.001 µM solutions of MNPs in 5 wt% TOPO/dodecane were prepared by subsequent dilution of the initial 1 µM MNP-solutions. To prepare mixtures with a fixed concentration of 0.1 µM of SNPs and a certain predetermined amount of MNPs, 20 µL of 1 µM SNP-solution and a certain amount of 0.1 µM, 0.01 µM or 0.001 µM MNP solution were mixed in a vial and topped up to 200 µL with 5 wt% TOPO/dodecane immediately prior to the PL-experiment. All of the samples in one measurement series were prepared from a single batch of particles. In a typical procedure a sample was prepared from 20 µL of 1 µM CdSe-NP solution mixed with 10 µL of a 0.01 µM 5nm-AuNP solution and then 170 µL of 5 wt% TOPO/dodecane were added to produce a 0.1 µM CdSeNP solution containing 0.5 % of 5 nm-AuDT relative to the CdSe-NP concentration. Characterization and PL measurements
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TEM measurements were performed on a Philips CM30 STEM (300 kV, LaB6-cathode) equipped with a GATAN digital camera. Images are recorded using Digital Micrograph. The particle core sizes were determined by measuring at least 150 individual particles from recorded TEM images. UV-Vis spectra were taken with a HP 8452A Diode Array Spectrophotometer and an Agilent 8453 UV-Vis. PL-spectra were recorded in a back-scattering geometry using a Renishaw inVia Raman microscope system. The excitation source is a green laser (λ = 532 nm) with an excitation power of This journal is © The Royal Society of Chemistry [year]
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Fig.2 All optical spectra of the particles used in the PL measurement series. The dotted arrow at 532 nm represents the excitation wavelength of the laser in the PL experiments The maxima from left to right: 4 nm AgNP, 418 nm (LSPR); 5 nm AuNP, 520 nm (LSPR); 5 nm CdSeHDA, 615 nm (absorption max.), 625 nm (emission max.); 7 nm CdSeOl, 640 nm (absorption max.), 652 nm (emission max.). All spectra are normalized (for a comparison of the extinction coefficients of AuNP and AgNP see Fig. 4).
agglomeration of the particles. Degradation of the particles should play a minor role as the particles used are all highly photostable and the excitation laser intensities are modest.
Results and Discussion 35
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Fig.1 TEM images (left) and optical spectra (right) of (a,b) 5 nm AuNP, (c,d) 4 nm AgNP, (e,f) 5 nm CdSeHDA and (g,h) 7 nm CdSeOl. The scale bars in the TEM images are 20 nm. The optical spectra of the CdSeNP are normalized.
~0.5 mW and a spot size of ~10 µm.. The emitted intensity is collected by the microscope objective (5x objective) and, after rejection of the elastically scattered laser light by a sharp edge filter, dispersed by the spectrometer and recorded using a CCD system. 40 µL of a sample are given into a homemade cylindrical vial which is sealed by a glass cover lid to avoid solvent evaporation. The PL-signal is maximized by focusing the laser inside the solution of 1 mm thickness prior to recording the spectra and at least three PL-spectra were recorded per sample at room temperature. The error bars in Figure 3 were determined by measuring 10 samples of the same solution in 10 different vials at given times. The relative error here is calculated to be δ = 0.3. We assign these deviations to slight variations in our specially made measuring vials and possible inhomogeneity in the solutions due to This journal is © The Royal Society of Chemistry [year]
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Representative TEM images and the optical spectra of the different particle samples used in the PL measurements are shown in Figure 1. The particles are nearly monodisperse with sizes of 4.9 ± 0.7 nm for CdSeHDA, 7.0 ± 0.6 nm for CdSeOl, 5.4 ± 0.5 nm for AuNP and 4.3 ± 0.9 nm for AgNP. The dispersity of the latter is higher, as the sample contains a small but considerable amount of larger particles with sizes around 10 nm. Nonetheless, the position of the plasmon resonance is hardly affected by this deviation in this size regime. The absorption maxima for AuNP and AgNP are 520 nm and 418 nm, respectively. 5 nm CdSeHDA show an absorption maximum at 615 nm and an emission maximum at 628 nm. For 7 nm CdSeOl the first absorption maximum is determined to be at 640 nm with an emission maximum at 653 nm. The optical spectra observed are in good agreement with the literature.31,33,34 First measurements where solutions of our particle mixtures were evaporated to dryness have shown a strong quenching of the photoluminescence even at low MNP concentrations, as the particle species are in close proximity in the dried films. This phenomenon was already observed in the literature35. To investigate the dependence of the optical properties on the distance between particles, solutions with different relative concentrations of MNPs and SNPs were prepared and their PL was measured. In this fashion series of samples based on MNPs with different plasmon bands and SNPs of different bandgap were studied in order to investigate the effect of overlap of the optical bands.
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Fig.3 PL spectra (left) and plots of PL intensity vs. MNP content (right, added MNP amount in nM; intensities are normalized to the sample with 0 nM MNP) of measurement series S1 (7nm-CdSeOl/4nm-AgOl; a,b), S2 (7nm-CdSeOl/5nm-AuDT; c,d) and S3 (5nm-CdSeHDA/5nm-AuDT; e,f. The concentration of the CdSeNP is 0.1 µM in all measurements 5
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The use of 5 wt% TOPO/dodecane as a solvent fulfills twopurposes. First, concentration changes due to evaporation during mixing of the samples and the measurements are reduced to a minimum because of the high boiling point of dodecane (bp = 240 °C). Second, the addition of 5 wt% TOPO ensures that CdSeNPs are always well stabilized. Three series of particle mixtures were used, each with a variation of the MNP content but fixed SNP concentration. The different particle species are chosen according to the relative energetic positions of their optical bands with respect to each other and to the excitation source (532 nm). The plasmon of the AuNP is resonantly excited by 532 nm light whereas that of the 4 nm AgNP is excited off resonance. The absorption and the emission bands of the lowest transition of both types of CdSeNP overlap with the plasmon band of the AuNP but the degree of overlap is larger for the 5 nm CdSeNP than for the 7 nm CdSeNP (Fig. 2). The first series (S1) consists of 7 nm-CdSeOl with admixed 4 nm-AgNP i.e the plasmon band and the lowest transitions of the This journal is © The Royal Society of Chemistry [year]
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SNP are spectrally well separated. The second and third series (S2, S3) are based on admixing 5 nm-AuNPs to 7 nm-CdSeOl (S2) and 5 nm CdSeHDA (S3), respectively, i.e. in both series the plasmon band is in resonance with the lowest transition of the SNP, but the degree of overlap is larger for the larger SNP because of their stronger absorption at 532 nm compared to the smaller SNP. In all three series, the concentration of the CdSeNP was fixed to 0.1 µM. The amount of metal-NPs was varied from 0-100 % of the CdSeNP concentration. The mean distance between nextneighbor pairs of SNP-MNP (the average distance measured from an SNP to its closest MNP neighbor) and MNP-MNP corresponds to the concentration of the MNP only. It can be calculated from the MNP concentration and is the same for both particle-pairings. In the three series it takes values between ~2.5 µm for the lowest investigated MNP concentration (at 0.1 nM) and ~100 nm for the highest investigated MNP concentration (0.1 µM). The SNP concentration of 0.1 µM (which is kept constant throughout the series) determines the [journal], [year], [vol], 00–00 | 4
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mean distance between next neighbor pairs of SNP-SNP as well as that of MNP-SNP (the average distance measured from an MNP to its closest SNP neighbor) yielding a value of ~100 nm for both. The PL spectra vs. the MNP content for the measurement series 7nm-CdSeOl/4nm-AgNP (S1), 7nm-CdSeOl/5nm-AuNP (S2), and 5nm-CdSeHDA/5nm-AuNP (S3) are shown in Fig. 3. There is no change in energetic position and full width at half maximum (FWHM) of the emission band with the MNP concentration in any of the cases. The presence of the MNP is only indicated by a change in the intensity of the PL band. The intensities in the plots are normalized to the intensities of the pure SNP samples. The three series all exhibit a higher PL-intensity for certain MNP concentrations than the corresponding pristine SNP colloidal solutions. For MNP concentrations higher than ~7.5% the relative PL intensity drops. The two series using AuNP (S2, S3) show a maximum enhancement of the PL by a factor of ~1.81.9. This is the case for 0.1% AuNP content in series S2 and for a content of 0.1-7.5 % AuNP in series S3. The observed enhancement is larger than the error of the measurement for S2 and S3 but not for S1. Here, a quenching of the luminescence is found which starts at a relative concentration of AgNP of 7.5 % and reduces the PL to 19 % of the initially observed intensity when the AgNP content is 50 %. This quenching of PL does also appear for series S2 at a relative concentration of 10 % AuNP but is not as pronounced as in the series S1. For series S3 at 100% AuNP content the PL is still as large as about 50 % of the initial intensity. Weaker luminescence enhancement occurs when AgNP are used instead of AuNP. Quenching of the PL is stronger for AgNP even at low concentrations. The different behavior of the two types of MNPs in this case arises from the different energetic positions of their respective plasmon resonance bands. With an excitation laser wavelength of 532 nm used in the experiments, the LSPR of the AuNP is resonantly excited near the 523 nm maximum. The AgNP show a resonance maximum at 420 nm and are therefore excited less by the incident light. CdSeNP show enhanced PL in the presence of resonantly excited AuNP when they are in dilute solution. The enhancement of the luminescence reaches about a factor of two and is strongest at a low AuNP content. When the AuNP content is raised above a certain threshold the enhancement vanishes and a slight quenching of the PL is observed. Only at high concentrations of the AuNP a significant quenching of the PL occurs.
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(1)
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where
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is the number of SNP in the ground state and is the number of SNP in the scattering volume. is the intensity of the incident laser light, is the absorption cross section of the SNP and is the recombination rate (which is determined by radiative and nonradiative recombination rates) of excitons in the SNP. In the case of low excitation energy and the approximation is justified. In the steady state regime the PL intensity can be calculated from the number of particles in state 1 using the radiative recombination rate from
(2) In the presence of MNP the transfer functions included so that the rate equation becomes
need to be
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Modelling of the PL Intensity Dependence To explain the measured dependence of the PL intensity on the MNP concentration we derive the rate equations for the system without and with added amounts of MNP. The behavior of the PL intensity in the series of samples can be derived by rate equations. The measured intensity curves are reproduced by comparing the results of the calculations for the system with different added amounts of MNP with that of the system without MNP. The measured intensity dependence can be explained qualitatively by the interplay of energy transfer processes between the particle species and the reabsorption of PL emission by the MNP (accounted for in the quantity ). It should be noted that the mechanisms of the transfer processes, in particular, within the
MNP subsystem, but also between MNP and SNP is not clear. For simplicity, we assume Förster resonant energy transfer processes (FT)36 between all the particles involved. The FT are described by the transfer functions , and where the subscript identifies the direction of the transfer (S=SNP and M=MNP). We also considered including the effect of the plasmon-enhanced field into the model function, but found that it is negligible because of the low particle density of the investigated system, i.e. the mean distances between MNP and SNP ( ). This finding is in agreement with the literature.37 and an The SNP are modelled as a system of a ground state excited state . The rate equation for the number of SNP in the first excited state can be approximated by
where the factor is an MNP and SNP concentration dependent correction to . Its physical meaning will be described further below. , and are the numbers of FTs between the particle types (4) (5) (6)
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which depend on the number of excited donor particles ( , ), the rate of FT between pairs of particles ( , , ) and the number of acceptor particles ( , ). is the number of MNP in the scattering volume and is the number of MNP in an excited state (plasmon oscillation) which is given in analogy to Eqs. (1) and (2) by
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(7) is the absorption cross-section of the MNP and is the rate of relaxation of the plasmon. FT is a direct energy transfer process between particle pairs. This energy transfer does not involve photons but is due to dipole-dipole-interactions only. Several studies suggest that plasmons can also act as donor and the term plasmon resonance energy transfer (PRET) has been coined.38–40 However, in this approximation, we describe the MNP as Förster donors. The FT rate can be defined as
(12)
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from a donor to an which states that the energy transfer rate acceptor is equal to the inverse lifetime of a donor exciton when the acceptor is at the critical distance from the donor where is the separation of donor and acceptor. In a dilute solution, all particles are distributed randomly. Therefore we can calculate the average FT rates (Eqs. 9 to 11) for our system by using the spherical particle density distribution of finding a particle at distance . describes the excitation transfer from the SNP emission band to the absorption band of the MNP at the emission wavelength, describes the excitation transfer from the plasmon of the MNP to an excited describes the resonant transfer of state of the SNP and excitation energy from one MNP to another. The rates are
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is the normalization, i.e. the probability to find the acceptor and is normalized to particle within the distances 1. The critical distances for the FT, , can be calculated from
where is the minimum separation of the particles, i.e. the thickness of the ligand shells (~1 nm) and is the radius of the scattering volume. 70
is an orientation factor of donor and acceptor where transition dipole moments ( in the case of randomly distributed, spherical and isotropic particles), is the quantum yield of the fluorescent donor, is the refractive index of the medium and
(14) is the overlap integral of donor emission spectrum and acceptor absorption spectrum .41 In a first approximation, we use the extinction spectra of the MNP as both the donor and acceptor optical densities and a donor strength , which we define as a fit parameter instead of the quantum yield for the calculation of . The calculated values for are given in Table 1. The correction function leads to a decrease of directly transferred excitation energy from MNP to SNP ( ) with increasing MNP content. The reason is the competing excitation transfer between the MNP themselves which becomes more probable with higher MNP density. This can be seen as energy storage within the MNP system for some time during which it is not available to the SNP system, hence the reduction in additional intensity is observed in the measurements. Eventually this stored energy is either lost as heat or transferred back to an SNP when such a transfer is preferable. However, as the energy transfer in the metal system is likely to be fast and efficient, the excitation energy can be distributed throughout the whole system and eventually may be transferred to an SNP that is located outside the detection volume. A photon emitted by such an SNP would therefore be lost to the measurement. Including all the quantities described above, the PL intensity of a mixture of SNP and MNP in the steady state regime can be calculated from Eq. (15) by
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where is the reabsorption of the PL emission by the MNP before it reaches the detector.
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The concentration dependence of the PL intensity is ultimately given by the ratio of :
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(16) where the substitutions
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and
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are the particle number densities and are the molar absorption coefficients of the SNP and MNP at the excitation wavelength, respectively. Eq. (16) now only contains quantities which are experimentally determinable or known from the literature. It provides a way to analytically predict the outcome of measurements, when the optical properties of the materials are known. If there is no energy transfer from MNP to SNP then and the inverse of Eq. 16 becomes the Stern-Volmer equation as
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the presence of the MNP themselves. Finally, the third process (P3) is the relaxation of all excitation coupled to the SNP system by radiative or nonradiative recombination paths, where the latter, in addition, include the energy transfer from SNP to MNP. P1 and P2 can lead to PL enhancement and are described by the nominator of the compound fraction. P3 includes the PL quenching that is described by the denominator of the compound fraction. Additionally, the absorption of PL emission by the MNP is included in Eq (16) in form of the term , but no such term for the excitation light is included, as we do not want to mix the approximations describing the MNP absorption at the excitation wavelength. To estimate the quantities to be used in Eq. (16), we first calculate the complex dielectric function of the MNP using the Drude free electron model and including the complex interband contributions of the bulk metals ,42,43
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where in our derivation a term is included that describes the absorption of the SNP PL emission by the MNP and the Stern-Volmer constant corresponds to
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with the damping constant, (19)
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is the plasma frequency, the scattering frequency where and the Fermi velocity of the bulk metal and the radius of the particle. In a non-absorbing medium with effective dielectric the polarizability of a metal sphere is defined as constant
(20) and the extinction cross-section is given by
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Fig.4 Calculated extinction efficiencies for 5 nm AuNP and 4 nm AgNP. The extinction efficiency is the ratio of the extinction cross-section to the geometrical cross-section πa2 of the particle. The shape and maxima of the functions are in good agreement with the measured spectra from UV-VIS-spectroscopy (ref. Figures 1 and 2).
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Basically, the compound fraction in Eq. (16) describes three nested processes that determine the PL intensity in the presence of MNP. The first process (P1) is the excitation of MNP by absorption of laser light. The second process (P2) is the energy transfer from MNP to SNP. However, this transfer is quenched by This journal is © The Royal Society of Chemistry [year]
This is valid in the electrostatic approximation when . We do not distinguish between the extinction cross-section and the absorption cross-section as the extinction of small metal particles is dominated by absorption and scattering is negligible, i. e. . The calculated extinction spectra for 5.4 nm AuNP and 4.3 nm AgNP are plotted in Fig. 4 where we used for Au and Ag, and for Ag, and for Au. The values for the effective medium were chosen such that the maxima of the calculated spectra appear at the values measured by UV-VIS spectroscopy. They are for AuNP and for AgNP. Note that the ligand-shell of the AuNP consists of dodecanethiol whereas that of the AgNP consists of oleic acid and the solvent is dodecane in both cases. Journal Name, [year], [vol], 00–00 | 7
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From the extinction cross-sections we calculate the molar extinction coefficients for AuNP and AgNP and from this the overlap integrals , where the SNP emission spectra were fit by Gaussian normal distributions and the SNP absorption spectra were rescaled to a literature value at their first absorption maximum.5 Using Lambert-Beer’s law the transmitted fraction of the emitted PL intensity at after reabsorption by the MNP with concentrations is calculated for S1-S3. Here we assume a light path length that equals half the height of the solution in the vial (L = 0.5 mm). (22)
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We have thus calculated a model function and the material properties to explain the intensity dependence of S1 to S3. Fig. 5 shows plots of the resulting intensity profiles calculated according to Eq. (16). The values for the quantities used in the calculations are given in Table 1. The fit parameters used are the quantum yield and the donor strength . Table 1 Calculated optical properties of the SNP and MNP in S1 to S3: (in 105 M-1cmCritical distances R, molar absorption coefficients 1 )and particle number density with the fit parameters quantum yield and donor strength for AgNP of 4.3 nm and AuNP of 5.4 nm in diameter, respectively..
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S1 4.3 nm Ag/ 7 nm CdSe
S2 5,4 nm Au/ 7 nm CdSe
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Fig. 5 Plots of the theoretical intensity dependence on the MNP concentration calculated from Eq. 16 with values given in Table 1for a) S1, b) S2 and c) S3 at c(SNP) = 0.1 µM (solid blue line), c(SNP) = 0.15 µM (blue dashed line) and c(SNP) = 0.05 µM (blue dotted line) and for the case that the MNP do not act as donors (black line); and the measured data at c(SNP) = 0.1 µM (black diamonds) along with the reabsorption
agree with the measurement when the experimentally determined particle sizes are used in the calculations. This suggests that the
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model function is appropriate and the interplay of FTs as we have described it, can be the reason for the observed PL enhancement and quenching behavior in (dilute) mixtures of SNP and MNP. It can be seen that the reabsorption of PL emission is negligible for the MNP concentrations (< 0.1 µM) used in the experiments and would only provide a significant contribution for much higher MNP density. When comparing the results of the calculations for case 1: MNP acting as donors and acceptors (blue lines in Fig. 5, ), with those of case 2: MNP only acting as acceptors, i.e. Stern-Volmer quenchers (black lines in Fig. 5, ), firstly; it can be seen that there is a dependence on the SNP density in the former case which is absent when case 2 is assumed. Secondly, the quality of the fit for S1 (Fig. 5a) is better when case 2 is assumed, it is almost the same for S2 (Fig. 5b) for either case 1 or case 2, and it is better for S2 (Fig. 5c) when case 1 is assumed. Nonetheless, the fit between theory and experiment is not as good as in the other cases. However, it may be concluded that for S1 the nonresonantly excited AgNP do not act as RET donors but still as strong RET acceptors (case 2) and the resonantly excited AuNP for S3 do act as RET donors and acceptors. In the model the reason for the PL enhancement in S2 and S3 at low MNP concentrations is the large ratio of absorption crosssections of MNP:SNP at the excitation wavelength and the FT from MNP to SNP. This is often described in the literature as an antenna effect of plasmonic particles.44 With increasing MNP content the FT from SNP to MNP becomes more efficient and the energy transfer from MNP to SNP is increasingly competing with the FT from MNP to MNP. The latter subsequently leads to a balance between the two FTs and therefore the additional energy available to the SNP saturates at some point and then decreases with further addition of MNP. At even higher MNP concentrations a quenching of the PL by the then dominant FT from SNP to MNP is the result. The FT depends on the overlap of the respective donor and acceptor optical bands. It is not necessarily the difference in energy between the band maxima that determines the efficiency of the FT but more importantly the absorption strength of the acceptor band and the quantum yield of the donor. The relative PL of the mixtures is nonlinear in both the concentration of the MNP and the concentration of the SNP (compare dashed and dotted lines in Fig. 5 for S1 to S3 and Eq. (16)). This is an interesting finding, as it suggests that, even when no PL enhancement can be measured directly, the observation of a dependence of the quenching on the SNP concentration should be due to an energy transfer from the quencher to the fluorophore and between the quenchers. However, it has to be stressed again that these are qualitative results. The deviations of theory and experiment can only be explained in part by the uncertainties of the MNP and SNP concentrations in the experiment or the size distribution of the MNP. The main reason for the differences between theory and experiment lies very likely in inappropriateness of the Förster mechanism for describing the energy transfer processes involving MNP. Therefore, to bring the theory presented to a more quantitative level, it is of primary importance to derive theoretical expressions for resonant energy transfer processes involving
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MNP, in addition to conducting further PL measurements using SNP of precisely determined quantum yield.
Conclusions
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In this article we have described the preparation of mixed colloidal solutions of MNPs (AuNP, AgNP) and SNPs (5-nmCdSeNP, 7-nm-CdSeNP) and performed PL measurements on the mixtures for varied MNP concentrations.. We have derived a rate-equation based model for the SNP PL taking into account reabsorption by the MNP as well as energy transfer processes between MNP and SNP and vice versa. The model is an extension of the well-known Stern-Vollmer model and sheds some light on to the interplay of the MNP and SNP in colloidal solutions which may either yield fluorescence quenching or fluorescence enhancement. The modelled dependence of the PL intensity of the SNP versus the concentration of added MNP allows one to interpret the measurements in detail. From our results it can be concluded that the PL of SNP in the proximity of MNP depends on electronic properties of the two types of particles as well as on the distance between the particles. In the model, enhancement appears when the absorptive power of the MNP is large compared to that of the SNP (at the excitation wavelength) and the overlap of the plasmon absorption with the band gap absorption of the SNP is large while there is only weak overlap with the Stokes-shifted band gap emission of the SNP. When the average distance between SNP and neighbor MNP falls below a critical value any enhancement is negated and quenching is observed because FT from SNP to MNP becomes dominant. Field enhancement due to the presence of the MNP seems to play a minor role at the mean particle distances studies > 100 nm in concordance with the literature.
Notes and references a Institute of Inorganic and Analytical Chemistry, Justus-LiebigUniversity Gießen, Heinrich-Buff-Ring 58, 35392 Giessen, Germany.. Fax: +49(0)641-99-34139; Tel: +49(0)641-99-34130; E-mail: [email protected] b Institute of Experimental Physics I, Justus-Liebig-University Giessen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany.. Fax: +49(0)641-9933139; Tel: +49(0)641-99-33190; E-mail: [email protected] † Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See DOI: 10.1039/b000000x/ ‡ Footnotes should appear here. These might include comments relevant to but not central to the matter under discussion, limited experimental and spectral data, and crystallographic data. 1. W. A. Murray and W. L. Barnes, Adv. Mater., 2007, 19, 3771–3782. 2. J. A. Creighton and D. G. Eadon, J. Chem. Soc. Faraday Trans., 1991, 87, 3881–3891. 3. W. W. Yu and X. Peng, Angew. Chem. Int. Ed., 2002, 41, 2368– 2371. 4. V. Biju, T. Itoh, A. Anas, A. Sujith, and M. Ishikawa, Anal. Bioanal. Chem., 2008, 391, 2469–2495. 5. W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater., 2003, 15, 2854–2860. 6. N. Gaponik, S. G. Hickey, D. Dorfs, A. L. Rogach, and A. Eychmüller, Small, 2010, 6, 1364–1378. 7. K. Tanabe, Energies, 2009, 2, 504–530.
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DOI: 10.1039/C4CP02347A
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Metal-enhanced Luminescence in Colloidal Solutions of CdSe and Metal Nanoparticles: Investigation of Density Dependence and Optical Band Overlap Christian Rohner,a Isabella Tavernaro,a Limei Chen,b Peter J. Klarb and Sabine Schlecht*a 5
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Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX DOI: 10.1039/b000000x The photoluminescence (PL) of semiconductor nanoparticles (SNP) is strongly modified when the semiconductor is in the proximity of a metal surface or a metal nanoparticle (MNP). The effect may be due to two different phenomena that are a) (Förster) resonant energy transfer ((F)RET) between semiconductor and metal and b) the enhanced electric field around metallic structures that arises from surface plasmon oscillations. Here we present experimental evidence of enhancement and quenching of the PL of dilute SNP colloidal solutions depending on the amount of admixed MNP and the position of the MNP plasmon band with respect to the excitation wavelength and the optical bands in the SNP. The average distance between an MNP and its next neighbor MNP is varied between ~0.1 and 2 µm by varying the MNP concentration, whereas those between MNP and SNP as well as between SNP and SNP are kept at about 0.1 µm. A model function based on the rate equations of the system is developed that yields a satisfactory description of the measured data by considering solely FRET between the particle species. The derived function is an extension to the Stern-Volmer equation, as it not only accounts for the energy transfer from the fluorescent SNPs to the MNPs, but also for the transfer of excitation from MNPs to SNPs and between MNPs. This theory provides a deeper insight into the mechanisms of metalenhanced fluorescence and fluorescence quenching phenomena.
Introduction
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The investigation of the optical properties of nanostructured materials is one of the fastest growing fields in science. In addition to their high surface to volume ratio, nanostructures exhibit phenomena which arise due to the tunable optical and electronic properties as a function of size and shape on the nanoscale. For example, metal nanoparticles (MNP) with diameters of 2-200 nm show a strong absorption and scattering of light in the visible range of the spectrum due to localized surface plasmon resonances (LSPR),1,2 and in semiconductor nanoparticles (SNP) the bandgap energy scales approximately inversely with the diameter squared of the particle due to quantum confinement effects, so that small particles of materials with bulk band gap energies in the infrared may show photoluminescence (PL) in the visible region of the spectrum.3–6 Thus, these materials' properties can be tuned to serve certain applications such as improving light harvesting in solar energy conversion,7,8 photocatalysis,9–11 bioanalytic spectroscopy12–14 and others. Recent publications show that there is an interaction between plasmonic structures and fluorophores that can lead to a quenching of the photoluminescence (PL) or to an enhancement of the intensity of the emitted light.15–19 It was found that the spatial distance between plasmonic structure and fluorophore and This journal is © The Royal Society of Chemistry [year]
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the energetic position of the plasmon resonance relative to the absorption and emission band maxima of the fluorophore play an important role.20–25 As of now, there are only few reports on PL enhancement or quenching being measured in solution, which provides a facile way to control the mean particle distance by a change of the particle concentration.21,26–29 In their recent work Li et al.26 describe concentration dependent PL enhancement of directly mixed, negatively charged CdTe NPs and negatively charged Au NPs in water, whereas the group of Lakowicz28 found only quenching of intensity when they mixed oppositely charged particles of the same two materials. In the former case the particles repulse each other and are therefore well separated, while in the latter SNPs and Au NPs form aggregates by electrostatic attraction. This indicates that there is a threshold distance as the separation of the particle species is reduced where the quenching of intensity becomes stronger than PL enhancement. In 2011 Li et al.21 reported metal-enhanced fluorescence of CdSe/ZnS core/shell particles conjugated with Au NPs by DNA oligonucleotide bridges in water with potential application in DNA detection. The distance between the particles could be controlled accurately over a range of a few nm by the number of bases in the oligonucleotide. A maximum enhancement was found when the distance between the particles was 11.9 nm, with
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a quenching of the fluorescence at shorter distance and almost no change in emission at larger distances up to 18.7 nm. The SNP with an emission maximum at 531 nm were excited at 420 nm and could in turn resonantly excite the AuNP LSPR which produced an enhanced local electric field around the Au particle. The result is explained by resonance energy transfer (RET) from SNP to Au NP at short distance and an enhanced intensity at intermediate distance by interaction of the enhanced local electric field with the SNPs. For even larger separation no interaction was found because the QDs could not excite the Au NPs plasmon resonantly and no RET from SNP to Au NP takes place. This leaves the open question whether there will be an enhancement at larger distances when the AuNP plasmon is resonantly excited by the excitation light. In order to further investigate these phenomena, we used dilute colloidal solutions containing SNPs as the fluorophore and metallic nanoparticles which show a distinct LSPR and measured the PL of the particle mixtures. As luminescent species CdSe NPs of different sizes and capped with trioctylphosphine, trioctylphosphine oxide, 1hexadecylamine and oleic acid (TOP/TOPO/HDA/Ol) were used and dodecanethiol-capped AuNP and oleic acid-capped AgNP were chosen as the plasmonic structures. The optical properties of the particles used can be adjusted by varying their size. This allows one to tune the overlap of the plasmon resonance band of the MNP and the absorption and emission band of the SNP and to investigate the influence of this overlap on the PL behavior.
Synthesis of 7 nm CdSe-NP capped TOP/TOPO/HDA/oleic acid (7 nm CdSeOl):
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All particles were synthesized according to well known procedures or slightly modified literature methods using standard Schlenk technique.30–32 Synthesis of 5 nm CdSe-NP capped TOP/TOPO/hexadecylamine (5 nm CdSeHDA):
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24.8 mg of AuPPh3Cl and 25 µL of DT were dissolved in 4 ml of benzene. 43.5 mg of tert-butylamine borane was added in one portion and the mixture was stirred at 55 °C for 1 h. The particles were then precipitated by addition of 25 ml of ethanol and purified as described above using ethanol instead of methanol to give ~1 ml of a 1 µM solution of 5 nm AuDT in 5 wt% TOPO/Dodecane.
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Synthesis of 4 nm AgNP capped with oleic acid:
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51.6 mg of 1,2-hexadecanediol were dissolved in 4 ml of 4-tertbutyltoluene at 120 °C under Ar atmosphere. A second solution of 22.1 mg of trifluoroacetate silver(I) salt and 320 µL oleic acid in 1 ml of 4-tert-butyltoluene was then injected into the first solution at 120 °C and stirred for 5 min. The mixture was allowed to cool to 60 °C and then 30 ml of ethanol were added to precipitate the particles. The product was purified as described above to give a 1 µM solution of AgNP in 5 wt% TOPO/dodecane.
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Preparation of particle mixtures for PL-measurements:
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5 g of TOPO and 3 g of HDA were mixed under argon atmosphere and the mixture was degassed at 120 °C for 30 min. The solution was then heated to 270 °C and a solution of 57.5 mg Cd(OAc)2 in 1.5 ml TOP was injected. The heating was removed and immediately after, a solution of 94.9 mg Se powder in 1.3 ml TOP was injected. After the temperature dropped to 180 °C the heating was reinstalled and the mixture was heated to 210 °C for 10 min. Then it was allowed to cool to 100 °C and diluted with 12 ml of dry toluene. Subsequently the particles were collected by precipitation with methanol and purification by a redispersion/centrifugation process using a hexane/methanol mixture. The product was dispersed in hexane, centrifuged again and separated from minor amounts of insoluble residue. A small sample was taken at that moment for TEM and UV-VIS analysis. The hexane solution is then dried under Argon flow and the particles were weighed. The diameter of the particles was determined from the TEM results and assuming a complete capping of the particles with no unbound ligand in the product the molar amount of particles was calculated. Finally the product was dissolved in an appropriate amount of 5 wt% TOPO/dodecane solution to give a 1 µM solution of the particles that was kept under air in a refrigerator until further use. The product is stable and shows PL for months.
51.4 mg of CdO, 1.15 mg of TOPO, 2.85 mg of HDA and 250 µL of oleic acid were mixed and the mixture was pumped at 120 °C for 30 min and the system flushed with argon. Then the clear solution was heated to 270 °C and a solution of 39.5 mg Se powder in 2.5 ml TOP was injected and the mixture heated for another 30 min. The product was then purified and a solution of predetermined concentration was prepared as described for 5 nm CdSeHDA. Synthesis of 5 nm AuNP capped with dodecanethiol:
Experimental section 30
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0.1 µM, 0.01 µM and 0.001 µM solutions of MNPs in 5 wt% TOPO/dodecane were prepared by subsequent dilution of the initial 1 µM MNP-solutions. To prepare mixtures with a fixed concentration of 0.1 µM of SNPs and a certain predetermined amount of MNPs, 20 µL of 1 µM SNP-solution and a certain amount of 0.1 µM, 0.01 µM or 0.001 µM MNP solution were mixed in a vial and topped up to 200 µL with 5 wt% TOPO/dodecane immediately prior to the PL-experiment. All of the samples in one measurement series were prepared from a single batch of particles. In a typical procedure a sample was prepared from 20 µL of 1 µM CdSe-NP solution mixed with 10 µL of a 0.01 µM 5nm-AuNP solution and then 170 µL of 5 wt% TOPO/dodecane were added to produce a 0.1 µM CdSeNP solution containing 0.5 % of 5 nm-AuDT relative to the CdSe-NP concentration. Characterization and PL measurements
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TEM measurements were performed on a Philips CM30 STEM (300 kV, LaB6-cathode) equipped with a GATAN digital camera. Images are recorded using Digital Micrograph. The particle core sizes were determined by measuring at least 150 individual particles from recorded TEM images. UV-Vis spectra were taken with a HP 8452A Diode Array Spectrophotometer and an Agilent 8453 UV-Vis. PL-spectra were recorded in a back-scattering geometry using a Renishaw inVia Raman microscope system. The excitation source is a green laser (λ = 532 nm) with an excitation power of This journal is © The Royal Society of Chemistry [year]
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Fig.2 All optical spectra of the particles used in the PL measurement series. The dotted arrow at 532 nm represents the excitation wavelength of the laser in the PL experiments The maxima from left to right: 4 nm AgNP, 418 nm (LSPR); 5 nm AuNP, 520 nm (LSPR); 5 nm CdSeHDA, 615 nm (absorption max.), 625 nm (emission max.); 7 nm CdSeOl, 640 nm (absorption max.), 652 nm (emission max.). All spectra are normalized (for a comparison of the extinction coefficients of AuNP and AgNP see Fig. 4).
agglomeration of the particles. Degradation of the particles should play a minor role as the particles used are all highly photostable and the excitation laser intensities are modest.
Results and Discussion 35
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Fig.1 TEM images (left) and optical spectra (right) of (a,b) 5 nm AuNP, (c,d) 4 nm AgNP, (e,f) 5 nm CdSeHDA and (g,h) 7 nm CdSeOl. The scale bars in the TEM images are 20 nm. The optical spectra of the CdSeNP are normalized.
~0.5 mW and a spot size of ~10 µm.. The emitted intensity is collected by the microscope objective (5x objective) and, after rejection of the elastically scattered laser light by a sharp edge filter, dispersed by the spectrometer and recorded using a CCD system. 40 µL of a sample are given into a homemade cylindrical vial which is sealed by a glass cover lid to avoid solvent evaporation. The PL-signal is maximized by focusing the laser inside the solution of 1 mm thickness prior to recording the spectra and at least three PL-spectra were recorded per sample at room temperature. The error bars in Figure 3 were determined by measuring 10 samples of the same solution in 10 different vials at given times. The relative error here is calculated to be δ = 0.3. We assign these deviations to slight variations in our specially made measuring vials and possible inhomogeneity in the solutions due to This journal is © The Royal Society of Chemistry [year]
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Representative TEM images and the optical spectra of the different particle samples used in the PL measurements are shown in Figure 1. The particles are nearly monodisperse with sizes of 4.9 ± 0.7 nm for CdSeHDA, 7.0 ± 0.6 nm for CdSeOl, 5.4 ± 0.5 nm for AuNP and 4.3 ± 0.9 nm for AgNP. The dispersity of the latter is higher, as the sample contains a small but considerable amount of larger particles with sizes around 10 nm. Nonetheless, the position of the plasmon resonance is hardly affected by this deviation in this size regime. The absorption maxima for AuNP and AgNP are 520 nm and 418 nm, respectively. 5 nm CdSeHDA show an absorption maximum at 615 nm and an emission maximum at 628 nm. For 7 nm CdSeOl the first absorption maximum is determined to be at 640 nm with an emission maximum at 653 nm. The optical spectra observed are in good agreement with the literature.31,33,34 First measurements where solutions of our particle mixtures were evaporated to dryness have shown a strong quenching of the photoluminescence even at low MNP concentrations, as the particle species are in close proximity in the dried films. This phenomenon was already observed in the literature35. To investigate the dependence of the optical properties on the distance between particles, solutions with different relative concentrations of MNPs and SNPs were prepared and their PL was measured. In this fashion series of samples based on MNPs with different plasmon bands and SNPs of different bandgap were studied in order to investigate the effect of overlap of the optical bands.
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Fig.3 PL spectra (left) and plots of PL intensity vs. MNP content (right, added MNP amount in nM; intensities are normalized to the sample with 0 nM MNP) of measurement series S1 (7nm-CdSeOl/4nm-AgOl; a,b), S2 (7nm-CdSeOl/5nm-AuDT; c,d) and S3 (5nm-CdSeHDA/5nm-AuDT; e,f. The concentration of the CdSeNP is 0.1 µM in all measurements 5
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The use of 5 wt% TOPO/dodecane as a solvent fulfills twopurposes. First, concentration changes due to evaporation during mixing of the samples and the measurements are reduced to a minimum because of the high boiling point of dodecane (bp = 240 °C). Second, the addition of 5 wt% TOPO ensures that CdSeNPs are always well stabilized. Three series of particle mixtures were used, each with a variation of the MNP content but fixed SNP concentration. The different particle species are chosen according to the relative energetic positions of their optical bands with respect to each other and to the excitation source (532 nm). The plasmon of the AuNP is resonantly excited by 532 nm light whereas that of the 4 nm AgNP is excited off resonance. The absorption and the emission bands of the lowest transition of both types of CdSeNP overlap with the plasmon band of the AuNP but the degree of overlap is larger for the 5 nm CdSeNP than for the 7 nm CdSeNP (Fig. 2). The first series (S1) consists of 7 nm-CdSeOl with admixed 4 nm-AgNP i.e the plasmon band and the lowest transitions of the This journal is © The Royal Society of Chemistry [year]
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SNP are spectrally well separated. The second and third series (S2, S3) are based on admixing 5 nm-AuNPs to 7 nm-CdSeOl (S2) and 5 nm CdSeHDA (S3), respectively, i.e. in both series the plasmon band is in resonance with the lowest transition of the SNP, but the degree of overlap is larger for the larger SNP because of their stronger absorption at 532 nm compared to the smaller SNP. In all three series, the concentration of the CdSeNP was fixed to 0.1 µM. The amount of metal-NPs was varied from 0-100 % of the CdSeNP concentration. The mean distance between nextneighbor pairs of SNP-MNP (the average distance measured from an SNP to its closest MNP neighbor) and MNP-MNP corresponds to the concentration of the MNP only. It can be calculated from the MNP concentration and is the same for both particle-pairings. In the three series it takes values between ~2.5 µm for the lowest investigated MNP concentration (at 0.1 nM) and ~100 nm for the highest investigated MNP concentration (0.1 µM). The SNP concentration of 0.1 µM (which is kept constant throughout the series) determines the [journal], [year], [vol], 00–00 | 4
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mean distance between next neighbor pairs of SNP-SNP as well as that of MNP-SNP (the average distance measured from an MNP to its closest SNP neighbor) yielding a value of ~100 nm for both. The PL spectra vs. the MNP content for the measurement series 7nm-CdSeOl/4nm-AgNP (S1), 7nm-CdSeOl/5nm-AuNP (S2), and 5nm-CdSeHDA/5nm-AuNP (S3) are shown in Fig. 3. There is no change in energetic position and full width at half maximum (FWHM) of the emission band with the MNP concentration in any of the cases. The presence of the MNP is only indicated by a change in the intensity of the PL band. The intensities in the plots are normalized to the intensities of the pure SNP samples. The three series all exhibit a higher PL-intensity for certain MNP concentrations than the corresponding pristine SNP colloidal solutions. For MNP concentrations higher than ~7.5% the relative PL intensity drops. The two series using AuNP (S2, S3) show a maximum enhancement of the PL by a factor of ~1.81.9. This is the case for 0.1% AuNP content in series S2 and for a content of 0.1-7.5 % AuNP in series S3. The observed enhancement is larger than the error of the measurement for S2 and S3 but not for S1. Here, a quenching of the luminescence is found which starts at a relative concentration of AgNP of 7.5 % and reduces the PL to 19 % of the initially observed intensity when the AgNP content is 50 %. This quenching of PL does also appear for series S2 at a relative concentration of 10 % AuNP but is not as pronounced as in the series S1. For series S3 at 100% AuNP content the PL is still as large as about 50 % of the initial intensity. Weaker luminescence enhancement occurs when AgNP are used instead of AuNP. Quenching of the PL is stronger for AgNP even at low concentrations. The different behavior of the two types of MNPs in this case arises from the different energetic positions of their respective plasmon resonance bands. With an excitation laser wavelength of 532 nm used in the experiments, the LSPR of the AuNP is resonantly excited near the 523 nm maximum. The AgNP show a resonance maximum at 420 nm and are therefore excited less by the incident light. CdSeNP show enhanced PL in the presence of resonantly excited AuNP when they are in dilute solution. The enhancement of the luminescence reaches about a factor of two and is strongest at a low AuNP content. When the AuNP content is raised above a certain threshold the enhancement vanishes and a slight quenching of the PL is observed. Only at high concentrations of the AuNP a significant quenching of the PL occurs.
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(1)
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where
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is the number of SNP in the ground state and is the number of SNP in the scattering volume. is the intensity of the incident laser light, is the absorption cross section of the SNP and is the recombination rate (which is determined by radiative and nonradiative recombination rates) of excitons in the SNP. In the case of low excitation energy and the approximation is justified. In the steady state regime the PL intensity can be calculated from the number of particles in state 1 using the radiative recombination rate from
(2) In the presence of MNP the transfer functions included so that the rate equation becomes
need to be
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(3)
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Modelling of the PL Intensity Dependence To explain the measured dependence of the PL intensity on the MNP concentration we derive the rate equations for the system without and with added amounts of MNP. The behavior of the PL intensity in the series of samples can be derived by rate equations. The measured intensity curves are reproduced by comparing the results of the calculations for the system with different added amounts of MNP with that of the system without MNP. The measured intensity dependence can be explained qualitatively by the interplay of energy transfer processes between the particle species and the reabsorption of PL emission by the MNP (accounted for in the quantity ). It should be noted that the mechanisms of the transfer processes, in particular, within the
MNP subsystem, but also between MNP and SNP is not clear. For simplicity, we assume Förster resonant energy transfer processes (FT)36 between all the particles involved. The FT are described by the transfer functions , and where the subscript identifies the direction of the transfer (S=SNP and M=MNP). We also considered including the effect of the plasmon-enhanced field into the model function, but found that it is negligible because of the low particle density of the investigated system, i.e. the mean distances between MNP and SNP ( ). This finding is in agreement with the literature.37 and an The SNP are modelled as a system of a ground state excited state . The rate equation for the number of SNP in the first excited state can be approximated by
where the factor is an MNP and SNP concentration dependent correction to . Its physical meaning will be described further below. , and are the numbers of FTs between the particle types (4) (5) (6)
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which depend on the number of excited donor particles ( , ), the rate of FT between pairs of particles ( , , ) and the number of acceptor particles ( , ). is the number of MNP in the scattering volume and is the number of MNP in an excited state (plasmon oscillation) which is given in analogy to Eqs. (1) and (2) by
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(7) is the absorption cross-section of the MNP and is the rate of relaxation of the plasmon. FT is a direct energy transfer process between particle pairs. This energy transfer does not involve photons but is due to dipole-dipole-interactions only. Several studies suggest that plasmons can also act as donor and the term plasmon resonance energy transfer (PRET) has been coined.38–40 However, in this approximation, we describe the MNP as Förster donors. The FT rate can be defined as
(12)
where
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(8)
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from a donor to an which states that the energy transfer rate acceptor is equal to the inverse lifetime of a donor exciton when the acceptor is at the critical distance from the donor where is the separation of donor and acceptor. In a dilute solution, all particles are distributed randomly. Therefore we can calculate the average FT rates (Eqs. 9 to 11) for our system by using the spherical particle density distribution of finding a particle at distance . describes the excitation transfer from the SNP emission band to the absorption band of the MNP at the emission wavelength, describes the excitation transfer from the plasmon of the MNP to an excited describes the resonant transfer of state of the SNP and excitation energy from one MNP to another. The rates are
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is the normalization, i.e. the probability to find the acceptor and is normalized to particle within the distances 1. The critical distances for the FT, , can be calculated from
where is the minimum separation of the particles, i.e. the thickness of the ligand shells (~1 nm) and is the radius of the scattering volume. 70
is an orientation factor of donor and acceptor where transition dipole moments ( in the case of randomly distributed, spherical and isotropic particles), is the quantum yield of the fluorescent donor, is the refractive index of the medium and
(14) is the overlap integral of donor emission spectrum and acceptor absorption spectrum .41 In a first approximation, we use the extinction spectra of the MNP as both the donor and acceptor optical densities and a donor strength , which we define as a fit parameter instead of the quantum yield for the calculation of . The calculated values for are given in Table 1. The correction function leads to a decrease of directly transferred excitation energy from MNP to SNP ( ) with increasing MNP content. The reason is the competing excitation transfer between the MNP themselves which becomes more probable with higher MNP density. This can be seen as energy storage within the MNP system for some time during which it is not available to the SNP system, hence the reduction in additional intensity is observed in the measurements. Eventually this stored energy is either lost as heat or transferred back to an SNP when such a transfer is preferable. However, as the energy transfer in the metal system is likely to be fast and efficient, the excitation energy can be distributed throughout the whole system and eventually may be transferred to an SNP that is located outside the detection volume. A photon emitted by such an SNP would therefore be lost to the measurement. Including all the quantities described above, the PL intensity of a mixture of SNP and MNP in the steady state regime can be calculated from Eq. (15) by
(15)
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where is the reabsorption of the PL emission by the MNP before it reaches the detector.
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The concentration dependence of the PL intensity is ultimately given by the ratio of :
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(16) where the substitutions
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and
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were made.
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are the particle number densities and are the molar absorption coefficients of the SNP and MNP at the excitation wavelength, respectively. Eq. (16) now only contains quantities which are experimentally determinable or known from the literature. It provides a way to analytically predict the outcome of measurements, when the optical properties of the materials are known. If there is no energy transfer from MNP to SNP then and the inverse of Eq. 16 becomes the Stern-Volmer equation as
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the presence of the MNP themselves. Finally, the third process (P3) is the relaxation of all excitation coupled to the SNP system by radiative or nonradiative recombination paths, where the latter, in addition, include the energy transfer from SNP to MNP. P1 and P2 can lead to PL enhancement and are described by the nominator of the compound fraction. P3 includes the PL quenching that is described by the denominator of the compound fraction. Additionally, the absorption of PL emission by the MNP is included in Eq (16) in form of the term , but no such term for the excitation light is included, as we do not want to mix the approximations describing the MNP absorption at the excitation wavelength. To estimate the quantities to be used in Eq. (16), we first calculate the complex dielectric function of the MNP using the Drude free electron model and including the complex interband contributions of the bulk metals ,42,43
(17)
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where in our derivation a term is included that describes the absorption of the SNP PL emission by the MNP and the Stern-Volmer constant corresponds to
(18) 50
with the damping constant, (19)
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is the plasma frequency, the scattering frequency where and the Fermi velocity of the bulk metal and the radius of the particle. In a non-absorbing medium with effective dielectric the polarizability of a metal sphere is defined as constant
(20) and the extinction cross-section is given by
(21)
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Fig.4 Calculated extinction efficiencies for 5 nm AuNP and 4 nm AgNP. The extinction efficiency is the ratio of the extinction cross-section to the geometrical cross-section πa2 of the particle. The shape and maxima of the functions are in good agreement with the measured spectra from UV-VIS-spectroscopy (ref. Figures 1 and 2).
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This is valid in the electrostatic approximation when . We do not distinguish between the extinction cross-section and the absorption cross-section as the extinction of small metal particles is dominated by absorption and scattering is negligible, i. e. . The calculated extinction spectra for 5.4 nm AuNP and 4.3 nm AgNP are plotted in Fig. 4 where we used for Au and Ag, and for Ag, and for Au. The values for the effective medium were chosen such that the maxima of the calculated spectra appear at the values measured by UV-VIS spectroscopy. They are for AuNP and for AgNP. Note that the ligand-shell of the AuNP consists of dodecanethiol whereas that of the AgNP consists of oleic acid and the solvent is dodecane in both cases. Journal Name, [year], [vol], 00–00 | 7
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From the extinction cross-sections we calculate the molar extinction coefficients for AuNP and AgNP and from this the overlap integrals , where the SNP emission spectra were fit by Gaussian normal distributions and the SNP absorption spectra were rescaled to a literature value at their first absorption maximum.5 Using Lambert-Beer’s law the transmitted fraction of the emitted PL intensity at after reabsorption by the MNP with concentrations is calculated for S1-S3. Here we assume a light path length that equals half the height of the solution in the vial (L = 0.5 mm). (22)
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We have thus calculated a model function and the material properties to explain the intensity dependence of S1 to S3. Fig. 5 shows plots of the resulting intensity profiles calculated according to Eq. (16). The values for the quantities used in the calculations are given in Table 1. The fit parameters used are the quantum yield and the donor strength . Table 1 Calculated optical properties of the SNP and MNP in S1 to S3: (in 105 M-1cmCritical distances R, molar absorption coefficients 1 )and particle number density with the fit parameters quantum yield and donor strength for AgNP of 4.3 nm and AuNP of 5.4 nm in diameter, respectively..
[nm]
a
S1 4.3 nm Ag/ 7 nm CdSe
S2 5,4 nm Au/ 7 nm CdSe
S3 5,4 nm Au/ 5 nm CdSe
13.31 (or 0)
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[nm]
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11.33
[nm] [10-8 nm-3]
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(532 nm)
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(628 nm)
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((653 nm)
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((532 nm)a
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0.05
1 (or 0)
1 (or 0)
1 (or 0)
Values for
are taken from the Lit.5
The plots in Fig. 5 show that the calculated curves qualitatively
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Fig. 5 Plots of the theoretical intensity dependence on the MNP concentration calculated from Eq. 16 with values given in Table 1for a) S1, b) S2 and c) S3 at c(SNP) = 0.1 µM (solid blue line), c(SNP) = 0.15 µM (blue dashed line) and c(SNP) = 0.05 µM (blue dotted line) and for the case that the MNP do not act as donors (black line); and the measured data at c(SNP) = 0.1 µM (black diamonds) along with the reabsorption
agree with the measurement when the experimentally determined particle sizes are used in the calculations. This suggests that the
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model function is appropriate and the interplay of FTs as we have described it, can be the reason for the observed PL enhancement and quenching behavior in (dilute) mixtures of SNP and MNP. It can be seen that the reabsorption of PL emission is negligible for the MNP concentrations (< 0.1 µM) used in the experiments and would only provide a significant contribution for much higher MNP density. When comparing the results of the calculations for case 1: MNP acting as donors and acceptors (blue lines in Fig. 5, ), with those of case 2: MNP only acting as acceptors, i.e. Stern-Volmer quenchers (black lines in Fig. 5, ), firstly; it can be seen that there is a dependence on the SNP density in the former case which is absent when case 2 is assumed. Secondly, the quality of the fit for S1 (Fig. 5a) is better when case 2 is assumed, it is almost the same for S2 (Fig. 5b) for either case 1 or case 2, and it is better for S2 (Fig. 5c) when case 1 is assumed. Nonetheless, the fit between theory and experiment is not as good as in the other cases. However, it may be concluded that for S1 the nonresonantly excited AgNP do not act as RET donors but still as strong RET acceptors (case 2) and the resonantly excited AuNP for S3 do act as RET donors and acceptors. In the model the reason for the PL enhancement in S2 and S3 at low MNP concentrations is the large ratio of absorption crosssections of MNP:SNP at the excitation wavelength and the FT from MNP to SNP. This is often described in the literature as an antenna effect of plasmonic particles.44 With increasing MNP content the FT from SNP to MNP becomes more efficient and the energy transfer from MNP to SNP is increasingly competing with the FT from MNP to MNP. The latter subsequently leads to a balance between the two FTs and therefore the additional energy available to the SNP saturates at some point and then decreases with further addition of MNP. At even higher MNP concentrations a quenching of the PL by the then dominant FT from SNP to MNP is the result. The FT depends on the overlap of the respective donor and acceptor optical bands. It is not necessarily the difference in energy between the band maxima that determines the efficiency of the FT but more importantly the absorption strength of the acceptor band and the quantum yield of the donor. The relative PL of the mixtures is nonlinear in both the concentration of the MNP and the concentration of the SNP (compare dashed and dotted lines in Fig. 5 for S1 to S3 and Eq. (16)). This is an interesting finding, as it suggests that, even when no PL enhancement can be measured directly, the observation of a dependence of the quenching on the SNP concentration should be due to an energy transfer from the quencher to the fluorophore and between the quenchers. However, it has to be stressed again that these are qualitative results. The deviations of theory and experiment can only be explained in part by the uncertainties of the MNP and SNP concentrations in the experiment or the size distribution of the MNP. The main reason for the differences between theory and experiment lies very likely in inappropriateness of the Förster mechanism for describing the energy transfer processes involving MNP. Therefore, to bring the theory presented to a more quantitative level, it is of primary importance to derive theoretical expressions for resonant energy transfer processes involving
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MNP, in addition to conducting further PL measurements using SNP of precisely determined quantum yield.
Conclusions
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In this article we have described the preparation of mixed colloidal solutions of MNPs (AuNP, AgNP) and SNPs (5-nmCdSeNP, 7-nm-CdSeNP) and performed PL measurements on the mixtures for varied MNP concentrations.. We have derived a rate-equation based model for the SNP PL taking into account reabsorption by the MNP as well as energy transfer processes between MNP and SNP and vice versa. The model is an extension of the well-known Stern-Vollmer model and sheds some light on to the interplay of the MNP and SNP in colloidal solutions which may either yield fluorescence quenching or fluorescence enhancement. The modelled dependence of the PL intensity of the SNP versus the concentration of added MNP allows one to interpret the measurements in detail. From our results it can be concluded that the PL of SNP in the proximity of MNP depends on electronic properties of the two types of particles as well as on the distance between the particles. In the model, enhancement appears when the absorptive power of the MNP is large compared to that of the SNP (at the excitation wavelength) and the overlap of the plasmon absorption with the band gap absorption of the SNP is large while there is only weak overlap with the Stokes-shifted band gap emission of the SNP. When the average distance between SNP and neighbor MNP falls below a critical value any enhancement is negated and quenching is observed because FT from SNP to MNP becomes dominant. Field enhancement due to the presence of the MNP seems to play a minor role at the mean particle distances studies > 100 nm in concordance with the literature.
Notes and references a Institute of Inorganic and Analytical Chemistry, Justus-LiebigUniversity Gießen, Heinrich-Buff-Ring 58, 35392 Giessen, Germany.. Fax: +49(0)641-99-34139; Tel: +49(0)641-99-34130; E-mail: [email protected] b Institute of Experimental Physics I, Justus-Liebig-University Giessen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany.. Fax: +49(0)641-9933139; Tel: +49(0)641-99-33190; E-mail: [email protected] † Electronic Supplementary Information (ESI) available: [details of any supplementary information available should be included here]. See DOI: 10.1039/b000000x/ ‡ Footnotes should appear here. These might include comments relevant to but not central to the matter under discussion, limited experimental and spectral data, and crystallographic data. 1. W. A. Murray and W. L. Barnes, Adv. Mater., 2007, 19, 3771–3782. 2. J. A. Creighton and D. G. Eadon, J. Chem. Soc. Faraday Trans., 1991, 87, 3881–3891. 3. W. W. Yu and X. Peng, Angew. Chem. Int. Ed., 2002, 41, 2368– 2371. 4. V. Biju, T. Itoh, A. Anas, A. Sujith, and M. Ishikawa, Anal. Bioanal. Chem., 2008, 391, 2469–2495. 5. W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater., 2003, 15, 2854–2860. 6. N. Gaponik, S. G. Hickey, D. Dorfs, A. L. Rogach, and A. Eychmüller, Small, 2010, 6, 1364–1378. 7. K. Tanabe, Energies, 2009, 2, 504–530.
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