Electronic energy migration in solid versus liquid host matrices for concentrated perylenediimide dye solutions

In this paper, we continue our evaluation of Forster-type theories of exciton diffusion in disordered environments. The perylenediimide dye Lumogen Red is used as a donor molecule in two different liquids, CHCl(3) and dimethylformamide, and the energy transfer to the acceptor molecule Rhodamine 700 is measured using time-resolved fluorescence decays. The exciton motion is measured over Lumogen Red concentrations ranging from 1 × 10(-4) to 5 × 10(-2) M, and the results are compared to previous results for exciton diffusion in a solid polymer. Depending on the theoretical approach used to analyze the data, we find that the energy migration in the liquids is a factor of 2-3 faster than in the solid polymer, even after taking molecular translation into account. Measurements for a Lumogen Red concentration of 10 mM in the different host environments yield diffusion constants ranging from 2.2 to 3.1 nm(2)/ns in the liquids, as compared to 1.1-1.2 nm(2)/ns in solid poly(methyl methacrylate) (PMMA). The results in the liquids are in good agreement with theoretical predictions and numerical simulations of previous workers, while the results in solid PMMA are 2-3 times slower. This discrepancy is discussed in the context of the rapid energetic averaging present in the liquid environments but absent in the solid matrix, where unfavorable configurations and low energy trapping sites are frozen in by the static disorder.     

Exciton migration by ultrafast Förster transfer in highly doped matrixes

The energy transfer between dye molecules and the mobility of the corresponding excitons are investigated in polymethyl methacrylate films highly doped with perylene bisimide dyes. The dynamics is measured by group delay corrected, femtosecond broad-band spectroscopy revealing the transfer route via absorption changes that are specific for the participating species. In films doped with 0.14 M perylene orange an ultrafast homotransfer between the dye molecules is found by analyzing the loss of the excitation-induced anisotropy. The process exhibits a stretched exponential time dependence which is characteristic for F?rster energy transfer between immobilized molecules. The transfer time is 1.5 ps for an average transfer distance of 2.3 nm and results in a high mobility of the optically generated excitons. In addition, we find that the excitons move to perylene orange dimers, which have formed in low concentration during the sample preparation. The observed energy transfer time is slightly shorter than expected for a direct F?rster transfer and indicates that exciton migration by multistep transfer between the monomers speeds up the transport to the dimers. In samples doped with perylene orange and perylene red heterotransfer to perylene red takes place with transfer times down to 600 fs. The mechanism is F?rster transfer as demonstrated by the agreement with calculations assuming electric dipole interaction between immobilized and statistically distributed donor and acceptor units. The model predicts the correct time dependence and concentration scaling for highly doped as well as diluted samples. The results show that ultrafast exciton migration between dye molecules in highly doped matrixes is an attractive and efficient mechanism to transport and collect energy in molecular systems and organic electronic devices. Further optimization should lead to a loss-free transport over distances typical for the thickness of active layers in these systems.     

Can luminescent quantum dots be efficient energy acceptors with organic dye donors?

We assessed the ability of luminescent quantum dots (QDs) to function as energy acceptors in fluorescence resonance energy transfer (FRET) assays, with organic dyes serving as donors. Either AlexaFluor 488 or Cy3 dye was attached to maltose binding protein (MBP) and used with various QD acceptors. Steady-state and time-resolved fluorescence measurements showed no apparent FRET from dye to QD. We attribute these observations to the dominance of a fast radiative decay rate of the donor excitation relative to a slow FRET decay rate. This is due to the long exciton lifetime of the acceptor compared to that of the dye, combined with substantial QD direct excitation.     

Excitation energy transfer between closely spaced multichromophoric systems: effects of band mixing and intraband relaxation

We theoretically analyze the excitation energy transfer between two closely spaced linear molecular J-aggregates, whose excited states are Frenkel excitons. The aggregate with the higher (lower) exciton band edge energy is considered as the donor (acceptor). The celebrated theory of F?rster resonance energy transfer (FRET), which relates the transfer rate to the overlap integral of optical spectra, fails in this situation. We point out that, in addition to the well-known fact that the point-dipole approximation breaks down (enabling energy transfer between optically forbidden states), also the perturbative treatment of the electronic interactions between donor and acceptor system, which underlies the F?rster approach, in general loses its validity due to overlap of the exciton bands. We therefore propose a nonperturbative method, in which donor and acceptor bands are mixed and the energy transfer is described in terms of a phonon-assisted energy relaxation process between the two new (renormalized) bands. The validity of the conventional perturbative approach is investigated by comparing to the nonperturbative one; in general, this validity improves for lower temperature and larger distances (weaker interactions) between the aggregates. We also demonstrate that the interference between intraband relaxation and energy transfer renders the proper definition of the transfer rate and its evaluation from experiment a complicated issue that involves the initial excitation condition. Our results suggest that the best way of determining this transfer rate between two J-aggregates is to measure the fluorescence kinetics of the acceptor J-band after resonant excitation of the donor J-band.     

Fluorescence resonance energy transfer between quantum dot donors and dye-labeled protein acceptors

We used luminescent CdSe-ZnS core-shell quantum dots (QDs) as energy donors in fluorescent resonance energy transfer (FRET) assays. Engineered maltose binding protein (MBP) appended with an oligohistidine tail and labeled with an acceptor dye (Cy3) was immobilized on the nanocrystals via a noncovalent self-assembly scheme. This configuration allowed accurate control of the donor-acceptor separation distance to a range smaller than 100 A and provided a good model system to explore FRET phenomena in QD-protein-dye conjugates. This QD-MBP conjugate presents two advantages: (1) it permits one to tune the degree of spectral overlap between donor and acceptor and (2) provides a unique configuration where a single donor can interact with several acceptors simultaneously. The FRET signal was measured for these complexes as a function of both degree of spectral overlap and fraction of dye-labeled proteins in the QD conjugate. Data showed that substantial acceptor signals were measured upon conjugate formation, indicating efficient nonradiative exciton transfer between QD donors and dye-labeled protein acceptors. FRET efficiency can be controlled either by tuning the QD photoemission or by adjusting the number of dye-labeled proteins immobilized on the QD center. Results showed a clear dependence of the efficiency on the spectral overlap between the QD donor and dye acceptor. Apparent donor-acceptor distances were determined from efficiency measurements and corresponding F?rster distances, and these results agreed with QD bioconjugate dimensions extracted from structural data and core size variations among QD populations.     

Fluorescence energy transfer-sensitized photobleaching of a fluorescent label as a tool to study donor-acceptor distance distributions and dynamics in protein assemblies: studies of a complex of biotinylated IgM with streptavidin and aggregates of concanavalin A

A photokinetic method of detection of fluorescence resonance energy transfer (FRET) between special fluorescent labels is applied to study time-averaged spatial distribution of labeled proteins in protein assemblies. Prolonged irradiation of a sample at the absorption maximum of the energy donor initiates FRET-sensitized fluorescence photobleaching of the energy acceptor label, which was monitored by steady-state fluorimetric measurements. Kinetics of the acceptor photobleaching and kinetics of decreasing the efficiency of FRET from donors to unbleached acceptors were determined. The FRET efficiency was found from measuring sensitization of acceptor fluorescence. Analysis of the photokinetic data permits to estimate the time-averaged distribution of acceptors on donor-acceptor distances in the range of characteristic distances of FRET. Dynamic processes influencing donor-acceptor distances can be also investigated by the method. Application of the method is demonstrated by the studies of a complex of biotinylated IgM with streptavidin and aggregates composed of concanavalin A and sodium dodecyl sulphate. A new thiadicarbocyanine dye was used as the acceptor label. R-phycoerythrin and tetramethylrhodamine isothiocyanate were the donor labels. In the IgM-streptavidin complex, 16% of acceptors most contributed to FRET provided 90% of FRET efficiency, whereas acceptors made about the same time-averaged contribution to FRET in the concanavalin A aggregates.     

Ultrafast energy transfer of one-dimensional excitons between carbon nanotubes: a femtosecond time-resolved luminescence study

Excitation energy transfer has long been an intriguing subject in the fields of photoscience and materials science. Along with the recent progress of photovoltaics, photocatalysis, and photosensors using nanoscale materials, excitation energy transfer between a donor and an acceptor at a short distance (≤1-10 nm) is of growing importance in both fundamental research and technological applications. This Perspective highlights our recent studies on exciton energy transfer between carbon nanotubes with interwall (surface-to-surface) distances of less than ～1 nm, which are equivalent to or shorter than the size of one-dimensional excitons in carbon nanotubes. We show exciton energy transfer in bundles of single-walled carbon nanotubes with the interwall distances of ～0.34 and 0.9 nm (center-to-center distances ～1.3-1.4 and 1.9 nm). For the interwall distance of ～0.34 nm (center-to-center distance ～1.3-1.4 nm), the transfer rate per tube from a semiconducting tube to adjacent semiconducting tubes is (1.8-1.9) × 10(12) s(-1), and that to adjacent metallic tubes is 1.1 × 10(12) s(-1). For the interwall distance of ～0.9 nm (center-to-center distance ～1.9 nm), the transfer rate per tube from a semiconducting tube to adjacent semiconducting tubes is 2.7 × 10(11) s(-1). These transfer rates are much lower than those predicted by the F?rster model calculation based on a point dipole approximation, indicating the failure of the conventional F?rster model calculations. In double-walled carbon nanotubes, which are equivalent to ideal nanoscale coaxial cylinders, we show exciton energy transfer from the inner to the outer tubes. The transfer rate between the inner and the outer tubes with an interwall distance of ～0.38 nm is 6.6 × 10(12) s(-1). Our findings provide an insight into the energy transfer mechanisms of one-dimensional excitons.     

Synthesis and spectroscopic properties of silica-dye-semiconductor nanocrystal hybrid particles

We prepared silica-dye-nanocrystal hybrid particles and studied the energy transfer from semiconductor nanocrystals (= donor) to organic dye molecules (= acceptor). Multishell CdSe/CdS/ZnS semiconductor nanocrystals were adsorbed onto monodisperse Sto?ber silica particles with an outer silica shell of thickness 2-23 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the energy transfer efficiency, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of nanocrystals with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with numerically calculated FRET efficiencies and by control experiments confirming attractive interaction between the nanocrystals and Texas Red freely dissolved in solution.     

Exciton diffusion and relaxation in methyl-substituted polyparaphenylene polymer films

Exciton diffusion in ladder-type methyl-substituted polyparaphenylene film and solution was investigated by means of femtosecond pump-probe spectroscopy using a combined approach, analyzing exciton-exciton annihilation, and transient absorption depolarization properties. We show that the different views on the exciton dynamics offered by anisotropy decay and annihilation are required in order to obtain a correct picture of the energy transfer dynamics. Comparison of the exciton diffusion coefficient and exciton diffusion radius obtained for polymer film with the two techniques reveals that there is substantial short-range order in the film. Also in isolated chains there is considerable amount of order, as revealed from only partial anisotropy decay, which shows that only a small fraction of the excitons move to differently oriented polymer segments. It is further concluded that interchain energy transfer is faster than intrachain transfer, mainly as a result of shorter interchain distances between chromophoric units.     

Novel "lipid-flow chip" configuration to determine donor-to-acceptor ratio-dependent fluorescence resonance energy transfer efficiency

We report on the determination of fluorescence resonance energy transfer (FRET) efficiency, which is dependent on the donor-to-acceptor (D-A) ratio, by using a new type of microchannel device called a "lipid-flow chip". The chip comprises two supported lipid bilayers (SLBs) that self-spread from either side of 10 microm wide straight lines and carry molecules embedded in them. We first show that the diffusion process that occurs when the two SLBs collide with each other in the channel and form a unified SLB can be expressed by a one-dimensional diffusion equation. Next we describe a method for determining the FRET efficiency between NBD (donor) and Texas Red (acceptor) from observations using the lipid-flow chip by employing a one-dimensional diffusion model. The advantages of our method are that all the D-A ratios are achieved in one chip, and a large number of data are recorded in one chip. The FRET efficiency varies depending on the D-A ratio under conditions whereby the concentration of the sum of the donors and acceptors is constant. The F?rster radius is also estimated from our results using a known model describing two-dimensional FRET systems, which yields a radius consistent with the previously reported value for NBD and Texas Red.     

Ultrafast fluorescence resonance energy transfer in a reverse micelle: excitation wavelength dependence

Fluorescence resonance energy transfer (FRET) from coumarin 480 (C480) to fluorescein 548 (F548) in a sodium dioctyl sulfosuccinate (AOT) reverse micelle is studied by picosecond and femtosecond emission spectroscopy. In bulk water, at the low concentration of the donor (C480) and the acceptor (F548), no FRET is observed. However, when the donor (C480) and the acceptor (F548) are confined in a AOT reverse micelle very fast FRET is observed. The time constants of FRET were obtained from the rise time of the emission of the acceptor (F548). In a AOT microemulsion, FRET is found to occur in multiple time scales--3, 200, and 2700 ps. The 3 ps component is assigned to FRET in the water pool of the reverse micelle with a donor-acceptor distance, 16 A. The 200 ps component corresponds to a donor-acceptor distance of 30 A and is ascribed to the negatively charged acceptor inside the water pool and the neutral donor inside the alkyl chains of AOT. The very long 2700 ps component may arise due to FRET from a donor outside the micelle to an acceptor inside the water pool and also from diffusion of the donor from bulk heptane to the reverse micelle. With increase in the excitation wavelength from 375 to 405 nm the relative contribution of the FRET due to C480 in the AOT reverse micelle (the 3 and 200 ps components) increases.     

Efficient light-harvesting,energy migration,and charge transfer by nanographene-based nonfullerene small-molecule acceptors exhibiting unusually long excited-state lifetime in the film state

Electron-acceptor small-molecules possessing a long exciton lifetime and a narrow energy band gap, opposing the energy gap law, are highly desirable for high-performance organic photovoltaics (OPVs) by realizing their efficient light-harvesting ability (LH), exciton diffusion (ED), and charge transfer (CT). Toward this goal, we designed an acceptor–donor–acceptor (A–D–A) type nonfullerene acceptor (NFA), TACIC, having an electron-donating, self-assembling two-dimensional (2D) nanographene unit, thienoazacoronene, at the center with electron-withdrawing groups at both ends. The TACIC film exhibited a narrow band gap (1.59 eV) with excellent LH. Surprisingly, the TACIC film showed an extremely long exciton lifetime (1.59 ns), suppressing undesirable nonradiative decay by its unique self-assembling behavior. When combined with a conjugated polymer donor, PBDB-T, slow ED and CT were observed (60 ps) with the excitation of TACIC owing to the large TACIC domain sizes. Nevertheless, the unusually high efficiencies of ED and CT (96% in total) were achieved by the long TACIC exciton lifetime. Additionally, unusual energy transfer (EnT) from the excited PBDB-T to TACIC was seen, demonstrating its dual LH role. The OPV device with PBDB-T and TACIC showed a high incident photon-to-current efficiency (IPCE) exceeding 70% at up to 710 nm and a power conversion efficiency of ∼10%. This result will open up avenues for a rational strategy of OPVs where LH, ED, and CT from the acceptor side as well as LH, EnT, ED, and CT from the donor side can be better designed by using 2D nanographene as a promising building block for high-performance A–D–A type NFAs.

A nonfullerene acceptor, TACIC, showed efficient light-harvesting, exciton diffusion, and charge transfer.     

Efficient exciton transport in layers of self-assembled porphyrin derivatives

The photosynthetic apparatus of green sulfur bacteria, the chlorosome, is generally considered as a highly efficient natural light-harvesting system. The efficient exciton transport through chlorosomes toward the reaction centers originates from self-assembly of the bacteriochlorophyll molecules. The aim of the present work is to realize a long exciton diffusion length in an artificial light-harvesting system using the concept of self-assembled natural chlorosomal chromophores. The ability to transport excitons is studied for porphyrin derivatives with different tendencies to form molecular stacks by self-assembly. A porphyrin derivative denoted as ZnOP, containing methoxymethyl substituents ({meso-tetrakis[3,5-bis(methoxymethyl)phenyl]porphyrinato}zinc(II)) is found to form self-assembled stacks, in contrast to a derivative with tert-butyl substituents, ZnBuP ({meso-tetrakis[3,5-bis(tert-butyl)phenyl]porphyrinato}zinc(II)). Exciton transport and dissociation in a bilayer of these porphyrin derivatives and TiO2 are studied using the time-resolved microwave conductivity (TRMC) method. For ZnOP layers it is found that excitons undergo diffusive motion between the self-assembled stacks, with the exciton diffusion length being as long as 15 +/- 1 nm, which is comparable to that in natural chlorosomes. For ZnBuP a considerably shorter exciton diffusion length of 3 +/- 1 nm is found. Combining these exciton diffusion lengths with exciton lifetimes of 160 ps for ZnOP and 74 ps for ZnBuP yields exciton diffusion coefficients equal to 1.4 x 10(-6) m2/s and 1 x 10(-7) m2/s, respectively. The larger exciton diffusion coefficient for ZnOP originates from a strong excitonic coupling for interstack energy transfer. The findings show that energy transfer is strongly affected by the molecular organization. The efficient interstack energy transfer shows promising prospects for application of such self-assembled porphyrins in optoelectronics.     

Transient Optical Characteristics of Broad Absorption Band Excitons Modulated by Micro-cavity

The understanding of light-matter interaction within micro-cavity lays the basic groundwork for many future photon-related technologies and applications. We prepared low quality metal-insulator-metal(MIM) micro-cavity consisting massive two-level broad absorption band dye(Nile Red) excitons, which randomly dispersed in SU-8 polymer negative resist matrix and measured their optical characteristics. New binate transmission peaks with large energy separation(so-called Rabi-splitting phenomenon) and their angular anti-crossing behavior in consequence of the interaction between dye excitons and confined photons were observed. It was also confirmed that the separated energy can be tuned by changing the doped exciton concentrations. Time-resolved transient absorption measurements showed that such an interaction is indeed a coherent one but rather a strong coupling one and one can modulate such a coherent mechanism by easily adjusting the detuning between dye excitons and confined cavity photons. This work may provide a comprehensive and deep understanding for such massive broad absoprtion band excitons-doped MIM micro-cavities and represent a further step to realize optical cavity-modulated devices in future.     

Accurate distance determination of nucleic acids via Förster resonance energy transfer: implications of dye linker length and rigidity

In Fo?rster resonance energy transfer (FRET) experiments, the donor (D) and acceptor (A) fluorophores are usually attached to the macromolecule of interest via long flexible linkers of up to 15 ? in length. This causes significant uncertainties in quantitative distance measurements and prevents experiments with short distances between the attachment points of the dyes due to possible dye-dye interactions. We present two approaches to overcome the above problems as demonstrated by FRET measurements for a series of dsDNA and dsRNA internally labeled with Alexa488 and Cy5 as D and A dye, respectively. First, we characterize the influence of linker length and flexibility on FRET for different dye linker types (long, intermediate, short) by analyzing fluorescence lifetime and anisotropy decays. For long linkers, we describe a straightforward procedure that allows for very high accuracy of FRET-based structure determination through proper consideration of the position distribution of the dye and of linker dynamics. The position distribution can be quickly calculated with geometric accessible volume (AV) simulations, provided that the local structure of RNA or DNA in the proximity of the dye is known and that the dye diffuses freely in the sterically allowed space. The AV approach provides results similar to molecular dynamics simulations (MD) and is fully consistent with experimental FRET data. In a benchmark study for ds A-RNA, an rmsd value of 1.3 ? is achieved. Considering the case of undefined dye environments or very short DA distances, we introduce short linkers with a propargyl or alkenyl unit for internal labeling of nucleic acids to minimize position uncertainties. Studies by ensemble time correlated single photon counting and single-molecule detection show that the nature of the linker strongly affects the radius of the dye's accessible volume (6-16 ?). For short propargyl linkers, heterogeneous dye environments are observed on the millisecond time scale. A detailed analysis of possible orientation effects (κ(2) problem) indicates that, for short linkers and unknown local environments, additional κ(2)-related uncertainties are clearly outweighed by better defined dye positions.     

Efficient Photoinduced Energy Transfer in a Newly Developed Hybrid SBA‐15 Photonic Antenna

A new hybrid photostable donor–acceptor mesoporous SBA‐15 silica system was designed and prepared. It consists of an encapsulated donor, the Super Yellow (SY) polymer, which transfers the photoexcitation energy directly to an acceptor dye that is linked outside the framework. The obtained composite material was characterized by X‐ray diffraction, nitrogen‐physisorption porosimetry, diffuse‐reflectance (DR)‐UV/Vis spectroscopy and photoluminescence, space‐ and time‐resolved confocal microscopy. The physico‐chemical analyses showed that the system behaves as an efficient Förster resonance energy transfer (FRET) pair, and high photoluminescence was observed from the acceptor. The presented photonic antenna is the first example of dye sensitization by polymer‐loaded mesoporous silica and represents a step forward in the search for new efficient and stable materials with opto‐electronic applications.     

Single lanthanide-doped oxide nanoparticles as donors in fluorescence resonance energy transfer experiments

We used lanthanide-ion doped oxide nanoparticles, Y(0.6)Eu(0.4)VO(4), as donors in fluorescent resonance energy transfer (FRET) experiments. The choice of these nanoparticles allows us to combine the advantages of the lanthanide-ion emission, in particular the long lifetime and the large Stokes shift between absorption and emission, with the detectability of the nanoparticles at the single-particle level. Using cyanine 5 (Cy5) organic molecules as acceptors, we demonstrated FRET down to the single-nanoparticle level. We showed that, due to the long donor lifetime, unambiguous and precise FRET measurements can be performed in solution even in the presence of large free acceptor concentrations. Highly efficient energy transfer was obtained for a large number of acceptor molecules per donor nanoparticle. We determined FRET efficiencies as a function of Cy5 concentration which are in good agreement with a multiple acceptor-multiple donor calculation. On the basis of the donor emission recovery due to acceptor photobleaching, we demonstrated energy transfer from single-nanoparticle donors in fluorescence microscopy experiments.     

Two-step FRET as a structural tool

The power of FRET to study molecular complexes is expanded by the use of two or more donor/acceptor pairs. A general theoretical framework for distance measurements in three-chromophore systems is presented. Three energy transfer schemes applicable to many diverse situations are considered: (I) two-step FRET relay with FRET between the first and second chromophores and between the second and third, (II) FRET from a single donor to two different acceptors, and (III) two-step FRET relay with FRET also between the first and third chromophores. Equations for the efficiencies involving multiple energy transfer steps are derived for both donor quenching and sensitized emission measurements. The theory is supported by experimental data on model systems of known structure using steady-state donor quenching, lifetime quenching, and sensitized emission. The distances measured in the three-chromophore systems agree with those in two-chromophore systems and molecular models. Finally, labeling requirements for diagnosis of the energy transfer scheme and subsequent distance measurements are discussed.     

The Excitation Spectra of Naphthalene Dimers: Frenkel and Charge‐transfer Excitons

Vertical electronic excitation energies have been calculated at the second‐order approximate coupled‐cluster (CC2) level for a series of dimeric naphthalene systems. The calculated excitation energies are compared with values obtained for a single naphthalene molecule and provide information about the coupling between the naphthalene moieties in the dimers. The calculations show that the coupling between the naphthalenes depends on the distance and the energy of the exciton. At long distances and high energies the excitons on the two naphthalenes are strongly coupled, whereas the excitation energies of the few lowest states are almost unaffected by the presence of the neighboring molecules. We have also analyzed the composition of the dimeric states that consist of the individual monomer states, to investigate the charge‐transfer (CT) and the Frenkel character of the excitons. Our results indicate that the CT exciton exists at short distances, and that its population drops as the distance between the two naphthalene increases.     

The effect of Brownian motion of fluorescent probes on measuring nanoscale distances by Förster resonance energy transfer

F?rster resonance energy transfer (FRET) is a powerful optical technique to determine intra-molecular distances. However, the dye rotational motion and the linker flexibility complicate the relationship between the measured energy transfer efficiency and the distance between the anchoring points of the dyes. In this study, we present a simple model that describes the linker and dye dynamics as diffusion on a sphere. Single-pair energy transfer was treated in the weak excitation limit, photon statistics and scaffold flexibility were ignored, and different time-averaging regimes were considered. Despite the approximations, our model provides new insights for experimental designs and results interpretation in single-molecule FRET. Monte Carlo simulations produced distributions of the inter-dye distance, the dipole orientation factor, κ(2), and the transfer efficiency, E, which were in perfect agreement with independently derived theoretical functions. Contrary to common perceptions, our data show that longer linkers will actually restrict the motion of dye dipoles and hence worsen the isotropic 2∕3 approximation of κ(2). It is also found that the thermal motions of the dye-linker system cause fast and large efficiency fluctuations, as shown by the simulated FRET time-trajectories binned on a microsecond time scale. A fundamental resolution limit of single-molecule FRET measurements emerges around 1-10 μs, which should be considered for the interpretation of data recorded on such fast time scales.