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Dec 2, 2008 - Probing Wave Functions at Semiconductor Quantum-Dot Surfaces by Non-FRET ... Eduard ZenkevichChristian von Borczyskowski. 2015,235- ...
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J. Phys. Chem. C 2008, 112, 20251–20257

20251

Probing Wave Functions at Semiconductor Quantum-Dot Surfaces by Non-FRET Photoluminescence Quenching Thomas Blaudeck,† Eduard I. Zenkevich,‡ Frank Cichos,§ and Christian von Borczyskowski* Institute of Physics and Center for Nanostructured Materials and Analytics (nanoMA), Chemnitz UniVersity of Technology, 09107 Chemnitz, Germany ReceiVed: August 21, 2008

Steady-state photoluminescence (PL) quenching of colloidal CdSe/ZnS and CdSe quantum dots (QDs) induced by functionalized porphyrin molecules was investigated for various QD sizes. The majority of the observed strong quenching of the QD photoluminescence can be assigned to neither Fo¨rster resonant energy transfer (FRET) nor photoinduced charge transfer between the QDs and the chromophore. Using the remaining small FRET efficiency to monitor the formation of QD/chromophore nanoassemblies, the major contribution to PL quenching was found to be proportional to the calculated quantum-confined exciton wave function at the QD surface. The quenching depends on the QD size and shell and is stronger for smaller quantum dots. Upon comparison of experimentally determined quenching rates and calculations of the exciton wave function, it was concluded that the attachment of only one chromophore induces a pertubation of the wave function that is accompanied by a strong increase of the radiationless decay rate. 1. Introduction During the past decade, colloidal quantum dots (QDs) from II-VI semiconductor materials such as CdSe have gained considerable interest because of their physical properties originating from quantum confinement.1 Applications such as QD lasers,2 biological markers,3 and anisotropic light emitters in photonic structures4 have been envisaged or even realized. Many of the applications make use of the tunability of the QD photoluminescence (PL) with QD diameter, but in each case, a high and stable quantum efficiency is mandatory. Whereas quantum confinement is basically understood, influences on the PL quantum efficiency are less evident but nevertheless crucial. In particular, the interplay with the environment and with the complex QD surface morphology is far from being understood. Colloidal QDs are bright emitters and are characterized by large absorption cross sections. However, their photoluminescence (PL) quantum efficiency has been found to be sensitive to a number of influences that originate either directly from the QD core5 or the QD surface6 or indirectly from the surrounding matrix.7 One of the fastest nonradiative recombination processes in QDs is an Auger-type process, in which the exciton interacts with a free charge in the QD core8 on time scales of 100 ps. Surface-related processes are slower and, in most cases, are influenced by the organic surfactant layer or surface defects.9 In this respect, PL decay times of less than 1 ns have been observed compared to radiative decay times longer than 10 ns.10 The influence of the surface on the PL quantum efficiency is usually diminished upon addition of a capping layer (for instance, ZnS).11 Further, nonradiative recombination processes are subject to fluctuations on time scales longer than about 10 * Corresponding author. Phone: +49.371.531.33035. Fax: +49 0.371.531. 21819. E-mail: [email protected]. † Present address: Institute for Print and Media Technology, Chemnitz University of Technology, 09107 Chemnitz, Germany. ‡ Present address: Department of Innovation Technologies and Robototechnique, National Technical University of Belarus, Minsk 220013, Belarus. § Present address: Molecular Nanophotonics, University of Leipzig, 04103 Leipzig, Germany.

ms.12 These slow changes might be related to fluctuations in the structure of the organic ligand shell6 or the local dielectric environment.13 Processes on a time scale of several milliseconds to several hundreds of s are known as PL intermittency (blinking) and are directly observed for single QDs.14,15 Blinking is related to a photoinduced charging of the QDs. Hence, PL intermittency is nothing else than a fluctuation of the PL quantum efficiency or the decay time, as has been shown experimentally.16,17 Furthermore, blinking is found to be sensitive to the dielectric environment,13,18 which, on one hand, further supports the charging hypothesis but also leads to the suggestion that a charge transfer with a subsequent self-trapping of charges in the surrounding dielectric environment might be the source of PL intermittency. Finally, processes related to blinking are directly related to reversible bleaching (photoluminescence quenching) of small QD ensembles.19,20 From these facts, it becomes obvious that the exciton in a QD is highly sensitive to local charges or distortions of the charge distribution. The excitonic wave function probes these local charges effectively because of its spatial extension. It is further evident that the time scale of these processes is related to that local volume (core, surface, and environment), which is responsible for the corresponding interaction process. Therefore, the PL quantum efficiency is sensitive to various interfaces, e.g., inorganic shell structures,21,22 and surfactants6,23-25 as long as the exciton wave function extends beyond the QD core. The effect of the solvent on the QD band gap, for example, has been investigated and attributed to the extension of the excitonic wave function into the dielectric environment.7 According to this background, it would be tempting to probe QD surface properties by distorting the interface with a welldefined local probe. Such controlled distortions will unravel microscopic details of either nonradiative processes occurring at the QD interface or the influence of chemical bonds at the QD surface through the importance of these processes for the emission intermittency of QD. Single molecules attached to the surface might act as such probes. Several experiments on the effects of organic molecules replacing the surfactant layer

10.1021/jp8074817 CCC: $40.75  2008 American Chemical Society Published on Web 12/02/2008

20252 J. Phys. Chem. C, Vol. 112, No. 51, 2008 have been reported.23-25 Experiments with a few or even only one single attached molecule are, aside from some recently reported results,26 missing. In this work, we show that direct surface labeling of a QD with only a few pyridyl-functionalized porphyrin molecules can reveal the nature of an as-yet microscopically unidentified PL quenching mechanism. We show that this quenching mechanism is related to neither FRET nor donor-acceptor charge transfer, which are generally considered as the main dynamic processes accompanying the formation of nanoassemblies. An extended knowledge of the influence of a few chromophores is not only of basic interest, for example, to understand PL intermittency, but is also important for applications that are based on QD/dye nanoassemblies for which a reduction of the influence of the surfactant dynamics has successfully been achieved by various means.20-24 However, when dealing with QDs as probes for dynamic processes taking place in the environment of a QD,26 stabilization of the PL quantum efficiency prohibits an intentional sensitivity to properties of the environment of the QD. Inspired by work on multiporphyrin arrays, a systematic study of direct labeling of colloidal semiconductor QDs with organic chromophores was performed26 that made use of the coordinating properties of the nitrogen lone-pair orbitals of the pyridyl as substituents of porphyrin molecules. Although part of the porphyrin-induced PL quenching could be explained by Fo¨rstertype resonant energy transfer (FRET) from the QDs to the attached porphyrin molecules,26 the majority of the PL quenching could recently not be assigned. In the present work, we show that the previously unidentified quenching mechanism can be uniquely assigned to the spatial extension of the exciton wave function and is thus related to the more general phenomenon of externally generated variations of the PL quantum efficiency. 2. Experimental Section In the present study, (5,10,15,20)-tetra-meta-pyridylporphyrin (m-Pyr)4-H2P was chosen as a probe molecule for CdSe QDs and CdSe core-shell QDs covered with two monolayers (2 ML) of ZnS. It is known26 that, among a series of pyridyl-substituted free-base porphyrins, (m-Pyr)4-H2P exhibits the most effective PL quenching of CdSe QDs upon titration. Figure 1 shows a schematic presentation of such a hetero nanoassembly consisting of a QD with a tri-n-octyl phosphine oxide (TOPO) surfactant layer and one (m-Pyr)4-H2P molecule attached via its mesopyridyl rings nearly perpendicular to the QD surface. Titration experiments were carried out by adding (m-Pyr)4-H2P to the QD solution at relative molar ratios x in toluene at ambient conditions. Details on the material properties can be found in the Supporting Information. The diameters, dCdSe, of the QDs varied between 2.1 and 5.2 nm, and in most cases, two capping ZnS monolayers were applied. CdSe Quantum Dots. The colloidal TOPO-capped CdSe and CdSe/ZnS quantum dots (CdSe core and CdSe/ZnS core-shell TOPO-Evidots TestKits) were obtained from Evident Technologies, Inc., Troy, NY. The molar absorption coefficients and core diameters of the quantum dots were calculated from the first exciton absorption peak according to Yu et al.27 The optical density of the QD starting solutions was adjusted to be lower than 0.1 at excitation and emission wavelengths in order to avoid nonlinear absorption and reabsorption effects. The concentrations varied in the range (1-10) × 10-7 M (cf. Supporting Information, Table A.I). The stability and purity of the QD solutions were checked by measuring the quantum yield stability at least 3 h after preparation.

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Figure 1. (A) Schematic representation (not to scale) of nanoassemblies formed by self-aggregation of pyridyl-functionalized porphyrin molecules on the CdSe/ZnS surface. The arrow indicates the direction of resonant energy transfer (FRET). (B) Enhancement of integrated fluorescence intensity of (m-Pyr)4-H2P upon addition to a solution of CdSe/ZnS QDs (dCdSe ) 3.0 nm/2 ML ZnS) (9) compared to a pure solution of (m-Pyr)4-H2P at same molar concentrations (0).

Pyridyl-Functionalized Porphyrin. (5,10,15,20)-Tetra-metapyridylporphyrin [(m-Pyr)4-H2P] was synthesized and purified according to known methods.28,29 For a characterization, see ref 30 and references therein. The porphyrin stock solution was prepared in toluene under ultrasonic treatment at 40 °C at concentrations in the range of (3-30) × 10-5 M. Titration Experiments. For all titration experiments, toluene (spectroscopic grade, Fluka SeccoSolv dried over molecular sieve) was used. The optical cuvettes (Hellma QS-111, path length ) 1 cm) and other glassware were flushed with acetone and ethanol, cleaned with aqueous H2SO4/H2O2, flushed with deionized water, dried in a nitrogen flow, and purged with toluene. In the titration experiments, the absorption and emission spectra of QD and (m-Pyr)4-H2P solutions were recorded with a Shimadzu 3001 UV/vis spectrometer and a Shimadzu RF5001PC spectrofluorophotometer, respectively. Aliquots of porphyrin were added in steps of 10-20 µL to QDs dispersed in 2.6 mL of toluene, giving molar ratios of x ) [(m-Pyr)4H2P]/[QD] ) 0.1-20. For the PL spectra, to keep direct excitation of (m-Pyr)4-H2P as low as possible, the QDs were excited at 465 nm, i.e., in the porphyrin absorption minimum between the Soret and Q-band absorptions. For quantitative comparison and reproducibility, it was necessary to perform experiments using exactly the same sample preparation procedures. All PL spectra were corrected for both detector sensitivity31,32 and dilution effects during the titration procedure. The residual QD emission intensity was numerically separated. The PL quantum efficiencies were determined in comparison with a quininsulphate dihydrate standard. Optical properties of the QDs in toluene were determined for a series of samples at ambient conditions. Data Analysis. For the analysis of the PL quenching curves as a function of the number of porphyrin molecules per QD, the well-known Stern-Volmer formalism33 was modified. In a more generalized approach, the luminescence quenching was described by

I0 )1+ I

∫0∞ K(x) dx

(1)

where I and I0 represent the PL emission intensity of the QD in presence and absence of the chromophores, respectively. In this

PL Quenching To Probe Wave Functions at QD Surfaces

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approach, the Stern-Volmer function K(x) depends explicitly on the molar concentration ratio of (m-Pyr)4-H2P to QDs and is expressed by the first derivative of the experimental data plotted in the Stern-Volmer representation. Further, the Stern-Volmer function, K(x), is expressed as

K(x) ) kqτ0

(2)

where the variable kq corresponds to the total quenching rate induced by quencher molecules and τ0 corresponds to the intrinsic PL lifetime of the QDs in the absence of the quencher molecules. For the smallest QDs, fluorescence lifetimes were extrapolated according to the literature.10 3. Results and Discussion As mentioned above, addition of (m-Pyr)4-H2P molecules to a solution of colloidal QDs results in a decrease of the quantumdot PL and an enhancement of the porphyrin fluorescence by Fo¨rster-type energy transfer.26,33 The contribution of resonant energy transfer (FRET) to the increasing (m-Pyr)4-H2P fluorescence (Figure 1B) was determined by standard procedures. As discussed later in detail, FRET is not the main source of PL quenching, but serves as a confirmation of the formation of QD/ porphyrin nanoassemblies. Figure 2 shows the PL intensity ratios, I/I0, of the QDs (Figure 2A) and the related Stern-Volmer presentation I0/I (Figure 2B) as a function of the porphyrin-to-QD molar ratio x. Figure 2C shows the effects of Fo¨rster resonant energy transfer (FRET) from the QDs to (m-Pyr)4-H2P. In Figure 3, the Stern-Volmer function, K(x), was obtained by numerical differentiation of the respective titration curves in the Stern-Volmer representation (see Figure 2B). The results are given for QDs of four different CdSe core diameters with two ZnS monolayers and one uncapped CdSe. The quenching curves (Figure 2A) clearly indicate that the integrated PL intensity decreases with increasing concentration of (m-Pyr)4-H2P. It is also immediately seen that, at the same molar ratio x, the quenching is more effective for smaller QDs than for larger ones. The Stern-Volmer plot, I0/I(x), of these results reveals a nearly linear behavior, suggesting that the quenching effect per molecule is approximately constant upon variation of x during the titration experiment. However, a closer look at K(x) (Figure 3) reveals that this linear behavior is only approximate. At a certain critical molar ratio (xc ) 1-6), K(x) becomes smaller by up to a factor of 2. Figure 3 thus suggests that quenching can be divided into at least two regimes that are separated by a crossover at a molar ratio around xc. Although there is some scatter in the data, the Stern-Volmer function K(x) can thus not be regarded as a constant over the entire range of molar ratios. In the frame of the Stern-Volmer analysis, the observation of K varying with the molar ratio x implies that the conditions for PL quenching undergo changes as a function of x itself. However, as quenching processes for x > xc are obviously of a more complex nature, we restrict the following considerations to molar ratios x < xc. This is a concentration range in which, on average, only a few molecules are attached to a QD and in which the total quenching rate kq is independent of x. As reported earlier26 for similar systems, the PL quenching in QD/porphyrin nanoassemblies (Figure 2A,B) is due to at least two contributions. The first, minor part can be attributed to Fo¨rster resonant energy transfer (FRET) from the QDs to (m-Pyr)4-H2P. The contribution of FRET to the total PL quenching is at most 10% and, hence, in most cases, is negligible. Nevertheless, we corrected for the FRET contribution when plotting K(x) in Figure

Figure 2. Typical titration curves for one uncapped (open markers) and four ZnS-capped (solid markers) CdSe QDs of various sizes with (m-Pyr)4-H2P in toluene. Typical experimental errors are shown for one size of QD. (A) Relative integrated PL emission intensity I(x)/I0 of the QDs as a function of the molar ratio x ) [(m-Pyr)4-H2P]/[QD]. (B) Stern-Volmer plot of part A [reciprocal relative PL emission intensity I0/I(x) of the QD]. (C) Efficiency of Fo¨rster resonant energy transfer (FRET) calculated on the basis of the approach in ref 26 from the integrated porphyrin fluorescence intensity (see Figure 1B). Legend: (0) dCdSe ) 3.5 nm/0 ML ZnS, (b) dCdSe ) 2.1 nm/2 ML ZnS, (9) dCdSe ) 3.0 nm/2 ML ZnS, (2) dCdSe ) 4.1 nm/2 ML ZnS, (() dCdSe ) 5.2 nm/2 ML ZnS.

3. Although it is small, this energy transfer is clear evidence for the formation of nanoassemblies. As is obvious from Figures 2 and 3, the second and major contribution to PL quenching, which had not previously been identified,26 depends dramatically on the size of the QD. Additionally, this quenching is not related to a photoinduced charge separation, as such a process would also result in quenching of the porphyrin fluorescence. According to eq 2, we analyzed the systematic behavior of the quenching process of type 2 as a function of QD size. In Figure 4, the quenching rate, kq, is plotted as a function of the QD core diameter of the respective QDs as obtained from the Stern-Volmer function at low molar ratios (see Figure 3). Data for τ0 are given in the Supporting Information. It is seen in Figure 4 that, for CdSe/ ZnS, kq follows a monotonic function that decays with QD core diameter. For comparison, CdSe QDs without a ZnS shell show a much stronger quenching than the respective core-shell analogue.

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Figure 3. Stern-Volmer function K(x) (cf. eq 1) at various molar ratios x for one uncapped (open markers) and four ZnS-capped (solid markers) CdSe quantum dots of various sizes upon titration with (mPyr)4-H2P in toluene. The results for each QD were obtained by numerical differentiation of the respective titration curves in the Stern-Volmer representation (Figure 2B) and were averaged over several runs. Typical experimental errors are shown for one QD size. Legend: (0) dCdSe ) 3.5 nm/0 ML ZnS, (b) dCdSe ) 2.1 nm/2 ML ZnS, (9) dCdSe ) 3.0 nm/2 ML ZnS, (2) dCdSe ) 4.1 nm/2 ML ZnS, (() d CdSe ) 5.2 nm/2 ML ZnS.

PL quenching of colloidal semiconductor QDs following surface attachment of organic molecules is reported frequently and has been assigned to either charge transfer34-36 or unspecified formation of surface-related trap states.36 However, in many of these cases, an unambiguous identification or microscopic understanding of the experimentally observed quenching is still missing. In the case of various porphyrin-type molecules, an effective charge transfer to the chromophore can be excluded, as no fluorescence quenching of the tentative charge acceptor (porphyrin) is observed.26,37,45 For this reason, we concentrate in the following discussion on the development of a microscopic model for the kind of PL quenching that is, with respect to attached chromophores, different from FRET or donor-acceptor charge transfer. Because we already showed in recent experiments that the detailed nature of the electronic structure of the various porphyrins can be neglected,38 we concentrate only on those aspects that are related directly to the outer interface of a QD as a function of size and shell thickness. We conjecture that, at the outer interface of the QD/porphyrin nanoassembly, two contributions are important: (i) the presence of “binding” orbitals that are the lone pair of a meso-pyridyl ring of the porphyrin and the Zn or Cd orbitals at the outer interface and (ii) the evanescent wave function of the confined exciton “leaking” out of the core (and the ZnS shell) of the QD. It is known from previous experiments26 that the porphyrin attaches to the surface in the manner shown in Figure 1. This implies that it is attached by at most two lone-pair nitrogen orbitals of the pyridyl rings, forcing the porphyrin macrocycle to be perpendicular to the QD surface. A nitrogen lone-pair orbital is considered to form a coordinating bond with Zn or Cd at the QD surface. Although the presence of lone pairs results in a quasi-binding of the pyridyl ring to the QD surface, this does not imply that a negative charge is transferred from the QD to the binding lone-pair orbitals because they are fully occupied. It is more likely, however, that partial negative charge can be transferred from the lone-pair orbital to the surface metal ions according to their electron affinity. As already mentioned, a charge transfer to or from the conjugated porphyrin chromophore would result in completely changed electronic and thus optical properties, which is not observed experimentally. Instead,

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Figure 4. (Left axis) Quenching rate kq averaged for x < xc of PL quenching induced by (m-Pyr)4-H2P for one uncapped and four ZnScapped CdSe QDs. (Right axis) Calculated size-dependent curves for the probability density functions Ψ2(r ) R + D) of a 1s electron at the outer interface (r ) R + D) between the ZnS shell and the environment for various ZnS shell thicknesses D for a potential barrier energy of 2 eV between the CdSe core and the ZnS shell, and a barrier energy of 4 eV between the ZnS shell and the matrix. Effective masses have been taken as 0.11 for the CdSe core and 0.28 for the ZnS shell, respectively. The constant C (see eq 3) has been adjusted with respect to Ψ2(R + D) to fit the experimental value at dCdSe ) 4.1 nm/2 ML ZnS. Legend: (0) dCdSe ) 3.5 nm/0 ML ZnS; (b) dCdSe ) 2.1 nm/2 ML ZnS; (9) dCdSe ) 3.0 nm/2 ML ZnS; (2) dCdSe ) 4.1 nm/2 ML ZnS; ((): dCdSe ) 5.2 nm/2 ML ZnS. dCdSe ) 2R corresponds to the CdSe core diameter and D to the ZnS layer thickness.

the attachment of the porphyrin meso-pyridyl ring is considered to change the charge density locally at or close to the outer interface of the QD, creating an image charge density in the QD itself.39 In other words, this might be described by the creation of a new surface state within the band gap. This local change of the charge distribution or formation of a surface state corresponds to the creation of an effective charge or trapping state seen by the subsequently excited exciton and will thus enhance nonradiative decay channels for the exciton decay. This will show up as PL quenching or a reduced quantum efficiency in accordance with current models for PL intermittency and PL quenching.15 An alternative, but fully equivalent description can be outlined as follows: Because the porphyrin molecules are very bulky, the formation of QD/dye nanoassemblies can be accomplished only by the release of more than two of the original surface ligands (TOPO). Such a replacement might create new uncoordinated Zn sites that subsequently act as trapping sites for the electron of the electron-hole pair. This explanation can be even more general. Each binding of an organic ligand and each dangling bond at a Zn or Cd atom at the surface is a local variation of the electrostatic potential that acts as a local trapping site for the electron of the electron-hole pair. The nature of the trap determines the strength of interaction of the electron-hole pair with this site. Thus, the removal of two to three TOPO molecules because of the binding of porphyrin could lead to an additional quenching of PL by creating unsaturated bonds. Moreover, the porphyrin macrocycle, as compared to a TOPO environment, might offer new local channels for self-trapping of charges. Related effects of the environment have been observed for the blinking phenomena of QDs and molecules.13,18 Yet how does the PL quenching shown in Figure 4 depend systematically on the size and ZnS shell of a QD? The key for understanding this observation is related to the quantum confinement itself. Quantum confinement of the exciton in its simplest version confines the wave function of the exciton (electron-hole pair) to a spherical box. As in any related

PL Quenching To Probe Wave Functions at QD Surfaces

J. Phys. Chem. C, Vol. 112, No. 51, 2008 20255 at the interface. The calculation of changes of electron densities therefore reduces to an evaluation of r2Ψ2(r) for the electron as a function of the CdSe core diameter and ZnS shell thickness. To account for the local character of this interaction at r ) R + D, where R ) 1/2dCdSe corresponds to the core radius and D corresponds to the ZnS shell thickness, r2Ψ2(r) has to be normalized with respect to r2, that is, with respect to the total QD surface area. This approximation holds because we are considering only pointlike interactions at the position of one nitrogen lone-pair orbital. Hence, the PL quenching rate becomes

kq(r) ) CΨ2(r)

(3) 2

Figure 5. (A) Scheme of the PL quenching model: Upon excitation, an electron-hole pair (exciton) is created in the CdSe core of the QD. The electron is delocalized over the core and the ZnS shell. As a result of the finite ZnS energy barrier EZnS, the electron can tunnel to the ZnS surface (and the environment). Because of the presence of a pyridyl-coordinated porphyrin molecule, the electron becomes partly localized in a volume element in the vicinity of the attachment site, described by Ψ2(r). (B) Logarithmic presentation of Ψ2(r) for a 1s electron in a core-shell spherical potential for five different sizes of QD with 0 or 2 ML of ZnS.

quantum mechanical problem, the wave function can extend beyond the imposed barrier, or in other words, the corresponding particle can tunnel through the barrier. Considering the hole and electron independently, as the confinement for the latter is much smaller because of its lower effective mass, one can safely assume that the tunnelling probability for the electron is higher than that for the hole. In core-shell QDs, the electron and hole have different potential landscapes and different effective masses. According to Dabbousi et al.,42 the barrier height between the core and shell for the electron is smaller than the total energy of the electron, and thus, the wave function extends well over the shell. The barrier for the hole is 2-3 times larger. Therefore, the hole has a lower probability of penetration into and across the shell. Thus, in the following discussion, we consider only the behavior of the electron wave function, especially how it behaves outside the QD, namely, at the interface with the functional pyridyl groups of the attached chromophore. The general scheme of our model is shown in Figure 5A. In addition to the coordination of a pyridyl ring to the surface, we show schematically the electron wave function at the outer interface of the QD. The chromophore attached to the surface locally modifies the electron wave function because of the presence of the nitrogen lone-pair orbital forming a surface state or a localization site (midband-gap state13) subsequently trapping the electron of the photogenerated exciton. We assume the particular influence of the nitrogen lone pair to be independent of the QD size. Then, all observed size dependence of the PL quenching (as expressed by the quenching rate, kq, in Figure 4) is directly related to the amplitude of the electron wave function

In particular, for the quantitative calculation of Ψ (r), we applied the particle-in-a-box model proposed for a core-shell QD according to Haus et al., solving the Schroedinger equation for an idealized QD with respect to the confinement eigenenergies.40 In this model, the effective mass, ma*, is assumed to be a material parameter that is a function of the radius R. We note that C contains all specific properties of the binding process and cannot be determined quantitatively in our model. In the case that the interaction of the chromophore at the interface cannot be approximated by a pointlike interaction, the constant C in eq 3 will have to be modified to C ) A/4πr2, where A corresponds an “effective molecular interaction area”. Figure 5B shows Ψ2(r) calculated for an s-type electron wave function for four CdSe/ZnS QDs with 2 ML of ZnS and one CdSe QD without a ZnS monolayer. For the calculations of Ψ2(r), we used energy barriers of 2 eV for the CdSe/ZnS interface41 and 4 eV for the ZnS/matrix interface42 and relative effective electron masses of 0.11, 0.28, and 1.00 in the CdSe core, confined ZnS shell, and surrounding matrix, respectively.43,44 It can be clearly seen that Ψ2(r) becomes smaller at the outer interface (marked by a circle) as the QD diameter increases. The corresponding value is largest for the uncapped CdSe QD (R ) 1.8 nm). Our results are quantitatively in close agreement with calculations by Leatherdale et al.,7 who considered solvent effects on optical band-gap energies. We can, however, neglect direct contributions to the band gap, as we did not observe any spectral shifts of the PL upon assembly formation.26,37,38 Correspondingly, in Figure 4, we compare the experimentally determined quenching rates, kq, in relation to the calculated value of Ψ2(r) as functions of both the QD core diameter, 2R, and the number of ZnS monolayers. The theoretical lines correspond to calculation of Ψ2(r) presented in Figure 5B, with a single value of the proportionality constant C determined in a way that the theoretical predictions for all QDs capped with 2 ML of ZnS agree with the experimental values most closely. It is clearly seen that the experimental quenching rates, kq, closely follow the calculated Ψ2(r) behavior for 2 ML of ZnS. Although our model works well for capped CdSe/ZnS QDs, the quenching rate for the uncapped CdSe QD is experimentally below the theoretically predicted value. The reason for this might be two-fold: (i) First, there might be differences in the binding constant of the chromophore: The Cd · · · N coordination is assumed to be weaker than Zn · · · N coordination, and thus, the average number of porphyrins attached to the surface will be smaller, resulting in reduced quenching. This implies that, compared to ZnS capping, we have to consider a smaller molar ratio x. If we were able to correct for this quantitatively, K(x) would increase toward values imposed by our model calculations. (ii) Calculating Ψ2(r) depends critically on the respective barrier energies at the interface, which are not known with high accuracy. Generally speaking, we thus expect that C varies with the capping.

20256 J. Phys. Chem. C, Vol. 112, No. 51, 2008 Altogether, the clear relationship between size-dependent PL quenching rates and calculated amplitudes of the exciton wave function strongly supports our model of a well-defined chromophore-induced quenching mechanism other than FRET and/ or photoinduced charge transfer. This good agreement between calculated and experimental data holds not only for the present series of experiments, but also for data obtained or reported previously (see Supporting Information). In fact, the dependence of PL quenching, induced at low molar ratios by only a single molecule, on the QD size and ZnS shell thickness clearly resembles the tunnelling of an electron (through the ZnS barrier) to the outer interface of the QD. Such tunnelling is followed by the (self-) localization of the electron-hole pair, which opens new nonradiative channels through enhanced electron-phonon coupling. The consequence is that the quantum efficiency of the subsequently photogenerated exciton is reduced. Thus, fluctuating bond formations at the surface (changes in local charge densities or formation of surface states) result in fluctuating quantum efficiencies of the QDs that are closely related to lifetime fluctuations and blinking observed for single quantum dots.14,16 It is thus intriguing to connect the observed PL quenching effects directly to processes that are relevant for the occurrence of blinking and related phenomena. The central interpretation of our results therefore is that already one or a few pointlike modifications in charge density in the surfactant layer (composed of ligands and the attached chromophore) will lead to local energy minima that force one of the charge carriers of the exciton to become localized. The participation of charges is strongly supported by the observation that porphyrin-induced PL quenching significantly increases as the polarity of the solvent is increased.26 In addition, previous nanosecond time-resolved PL experiments showed that, upon formation of nanoassemblies (in which only a few porphyrins are involved), the overall reduction of the quantum efficiency is accompanied by a shift of the nonexponential PL decay kinetics toward shorter decay times.26,37 We stress again that the presently identified mechanism for PL quenching is completely distinct from the mechanism of charge transfer among the involved moieties upon photoexcitation of a QD (or of an attached chromophore). Because we have assigned the origin of PL quenching to the tunnelling of a charge from the QD to a position close to the meso-pyridyl nitrogen of the porphyrin attached to the QD surface, the question might arise as to whether the quenching can be described merely by the interaction of the exciton wave function with the pyridyl part of the porphyrin chromophore. To answer the question of whether the PL quenching of the QD really needs the attachment of the porphyrin chromophore or requires just the pyridine substituent, we directly compared the PL quenching effects induced by titration with pyridine and with monopyridyl-substituted porphyrin molecules [(m-Pyr)1H2P]. The results are shown in Figure 6. It turns out that a small (2-3%) decrease of the PL quantum efficiency of the QD is due to dilution by toluene (0) during the titration procedure. Essentially the same quenching is observed for titration by pyridine (9). In comparison, for molar ratios x ) 1-8, the PL quenching of a QD by monopyridyl-substituted porphyrin [(mPyr)1-H2P, which has one pyridyl ring] is considerably stronger than in the above two cases (k). The reasons for this behavior might be as follows: (i) van der Waals interactions between TOPO molecules and the large (in comparison with pyridine) porphyrin molecule might favor a strong incorporation of a porphyrin molecule into the QD interface. (ii) The weak solubility of (m-Pyr)1-H2P in toluene might also favor fixation

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Figure 6. PL quenching of colloidal CdSe/ZnS QDs (dCdSe ) 2.1 nm) induced by (m-Pyr)1-H2P (k) and pyridine (9). For comparison, PL quenching by addition of pure toluene is indicated (0). Note that the PL change due to the change in concentration upon addition of the aliquot is already taken into account.

on the QD surface. (iii) The electronic properties of the π-conjugated porphyrin macrocycle might influence the local charge distribution close to the position of the interacting pyridine lone pair at the QD surface.38,45 However, it should be mentioned that, at the same molar ratio x ) [H2P]/[QD], the PL quenching of tetra-pyridyl-containing (m-Pyr)4-H2P is essentially stronger (compare Figure 2) than that observed for (m-Pyr)1-H2P (Figure 6). As we have shown recently for CdSe/ZnS QDs, the PL quenching efficiency, and thus the probability of forming QD/porphyrin nanoassemblies, decreases with increasing number of pyridyl rings.26,37 Moreover, the stability of a two-point interaction is stronger than the stability of a one-point interaction. This observation might imply that pyridine is only loosely fixed to the QD surface at sufficient low molar ratios. Thus, the experiments reveal that there is almost no PL quenching of CdSe/ZnS QDs by pyridine even at 100 times increased relative molar ratios. This observation prompts us to believe that the porphyrin chromophore itself is of central importance (argument iii), although the specific electronic structure is of much less influence.38 Recent investigations on similarly attached perylene diimide chromophores support this statement.46 4. Conclusions In summary, we have shown that the PL of CdSe QDs is quenched upon the formation of nanoassemblies with pyridylfunctionalized porphyrin molecules in solution even at a 1:1 molar ratio. The related PL quenching rate, kq, scales inversely with the QD diameter and can be understood in terms of a tunnelling of the electron (of the excited electron-hole pair) followed by a (self-) localization of the electron or the formation of surface states. These observations are in line with the microscopic understanding of blinking phenomena of single QDs. The difference is that, in the present experiments, the charge-density modifications have only pointlike (local) character. Our findings highlight that single functionalized molecules can be considered as probes for the complex interface physics and dynamics of colloidal semiconductor QDs. A detailed understanding of PL properties on a microscopic level is essential for describing optical properties such as PL intermittency, which so far limit applications of QDs. Additionally, our findings offer a new perspective with respect to PL quenching experiments, which very often assign quenching to FRET or photoinduced charge-transfer processes between donor and acceptor assemblies. Such an assignment, however, makes the identification of the related processes on both constituents mandatory.

PL Quenching To Probe Wave Functions at QD Surfaces Acknowledgment. Porphyrin has been synthesized and characterized by Dr. A. M. Shulga (National Technical University of Belarus, Minsk, Belarus). We thank Prof. Dr. S. V. Gaponenko (National Technical University of Belarus, Minsk, Belarus) for fruitful discussions during article preparation and M. Heiderna¨tsch (TU Chemnitz, Chemnitz, Germany) for assistance with the simulations. This work was funded by the German Science Foundation (DFG, Graduate College 829), the Volkswagen Foundation (Priority Program “Physics, Chemistry and Biology with Single Molecules”), the Belarus Complex Program for Scientific Research (KMS-17 Nanotech 6.18), INTAS (Grant 03-50-4540), and the German Academic Exchange Service (DAAD, Grant A/08/08573). We also thank the reviewers for valuable comments and suggestions. Supporting Information Available: Detailed summary of the results and additional information on the quantum-mechanical model. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Alivisatos, A. P. Science 1996, 271, 933–937. (2) Eisler, H. J.; Sundar, V. C.; Bawendi, M. G.; Walsh, M.; Smith, H. I.; Klimov, V. I. Appl. Phys. Lett. 2002, 80, 4614–4616. (3) Chan, W. C. W.; Nie, S. M. Science 1998, 281, 2016–2018. (4) Barth, M.; Schuster, R.; Gruber, A.; Cichos, F. Phys. ReV. Lett. 2006, 96, 243902. (5) Labeau, O.; Tamarat, P.; Lounis, B. Phys. ReV. Lett. 2003, 90, 257404. (6) Wuister, S. F.; de Mello Donega, C.; Meijerink, A. J. Phys. Chem. B 2004, 108, 17393–17397. (7) Leatherdale, C. A.; Bawendi, M. G. Phys. ReV. B 2001, B 63, 165315. (8) Neuhauser, R. G.; Shimizu, K. T.; Woo, W. K.; Empedocles, S. A.; Bawendi, M. G. Phys. ReV. Lett. 2000, 85, 3301–3304. (9) Yu, W. W.; Wang, Y. A.; Peng, X. Chem. Mater. 2003, 15, 4300– 4308. (10) Javier, A.; Magana, D.; Jennings, T.; Strouse, G. F. Appl. Phys. Lett. 2003, 83, 1423–1425. (11) Hines, M. A.; Guyot-Sionnest, P. J. Phys. Chem. 1996, 100, 468– 471. (12) Smith, A. M.; Duan, H. W.; Rhyner, M. N.; Ruang, G.; Nie, S. M. Phys. Chem. Phys. 2006, 8, 3895–3903. (13) Issac, A.; von Borczyskowski, C.; Cichos, F. Phys. ReV. B 2005, 71, 161302. (14) Nirmal, M.; Dabbousi, B. O.; Bawendi, M. G.; Macklin, J. J.; Trautman, J. K.; Harris, T. D.; Brus, L. E. Nature 1996, 383, 802–804. (15) Cichos, F.; von Borczyskowski, C.; Orrit, M. Curr. Opin. Colloid Interface Sci. 2007, 12, 272. (16) Schlegel, G.; Bohnenberger, J.; Potapova, I.; Mews, A. Phys. ReV. Lett. 2002, 88, 137401. (17) Shimizu, K. T.; Woo, W. K.; Fisher, B. R.; Eisler, H. J.; Bawendi, M. G. Phys. ReV. Lett. 2002, 89, 117401. (18) Schuster, J.; Cichos, F.; von Borczyskowski, C. Appl. Phys. Lett. 2005, 87, 051915.

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