Fluorescence resonance energy transfer (FRET) in chemistry and biology: Non-F?rster distance dependence of the FRET rate

Fluorescence resonance energy transfer (FRET) is a popular tool to study equilibrium and dynamical properties of polymers and biopolymers in condensed phases and is now widely used in conjunction with single molecule spectroscopy. In the data analysis, one usually employs the F?rster expression which predicts (l/R ⁶) distance dependence of the energy transfer rate. However, critical analysis shows that this e_xpression can be of rather limited validity in many cases. We demonstrate this by explicitly considering a donor-acceptor system, polyfluorene (PF₆)-tetraphenylporphyrin (TPP), where the size of both donor and acceptor is comparable to the distance separating them. In such cases, one may expect much weaker distance (as l/R ² or even weaker) dependence. We have also considered the case of energy transfer from a dye to a nanoparticle. Here we find l/R ⁴ distance dependence at large separations, completely different from F?rster. We also discuss recent application of FRET to study polymer conformational dynamics. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

A Brief Overview of Some Physical Studies on the Relaxation Dynamics and Förster Resonance Energy Transfer of Semiconductor Quantum Dots

This article highlights some physical studies on the relaxation dynamics and Förster resonance energy transfer (FRET) of semiconductor quantum dots (QDs) and the way these phenomena change with size, shape, and composition of the QDs. The understanding of the excited‐state dynamics of photoexcited QDs is essential for technological applications such as efficient solar energy conversion, light‐emitting diodes, and photovoltaic cells. Here, our emphasis is directed at describing the influence of size, shape, and composition of the QDs on their different relaxation processes, that is, radiative relaxation rate, nonradiative relaxation rate, and number of trap states. A stochastic model of carrier relaxation dynamics in semiconductor QDs was proposed to correlate with the experimental results. Many recent studies reveal that the energy transfer between the QDs and a dye is a FRET process, as established from 1/d⁶ distance dependence. QD‐based energy‐transfer processes have been used in applications such as luminescence tagging, imaging, sensors, and light harvesting. Thus, the understanding of the interaction between the excited state of the QD and the dye molecule and quantitative estimation of the number of dye molecules attached to the surface of the QD by using a kinetic model is important. Here, we highlight the influence of size, shape, and composition of QDs on the kinetics of energy transfer. Interesting findings reveal that QD‐based energy‐transfer processes offer exciting opportunities for future applications. Finally, a tentative outlook on future developments in this research field is given.     

The photoluminescent graphene oxide serves as an acceptor rather than a donor in the fluorescence resonance energy transfer pair of Cy3.5-graphene oxide

We have systematically studied the fluorescence resonance energy transfer (FRET) efficiency between the photoluminescent graphene oxide (GO) and Cy3.5 dye by controlling the donor-acceptor distance with a double stranded DNA and demonstrated that the GO serves as an acceptor rather than a donor in this FRET system.     

Rate of excitation energy transfer between fluorescent dyes and nanoparticles

Because of the sensitivity of the rate of Coulomb interaction induced long range resonance energy transfer (RET) on the distance between the donor (D) and the acceptor (A) molecules, the technique of FRET (fluorescence resonance energy transfer) is popularly termed as “spectroscopic ruler” and is increasingly being used in many areas of biological and material science. For example, the phenomenon is used to monitor the in vivo separation between different (bio)polymers/units of (bio)polymers and hence the dynamics of various biomolecular processes. In this work, we examine the distance and the orientation dependence of RET in three different systems: (i) between a conjugated polymer and a fluorescent dye, (ii) between a nanometal particle (NMP) and a fluorescent dye and (iii) between two NMP. We show that in all the three cases, the rate of RET follows a distance dependence of d^−σ where exponent σ approaches 6 at large distance d (Förster type dependence) but has a value varying from 3–4 at short to intermediate distances.     

Electronic mechanism of STM-induced diffusion of hydrogen on Si(100)

We have observed a scanning tunneling microscopy (STM) induced lateral transfer of a single hydrogen atom on the Si(100) surface. The transfer rate of the hydrogen atom is proportional to the electron dose, indicating an electron-assisted transfer mechanism. Measurements of the relations between the transfer rate and the sample bias and temperature give further support for an electronic mechanism. The bias dependence of the transfer rate shows a peak, and from a first principles electronic structure calculation we show that the position of the peak is related to the energy of a localized surface resonance. We propose that the hydrogen transfer is related to inelastic hole scattering with this surface resonance. We develop a microscopic model for the hydrogen transfer, and using the experimental data we extract information on the resonance lifetime and the transfer yield per resonant electron. The transfer takes place by tunneling through a small excited state transfer barrier. The transfer rate is increased if the hydrogen atom before the resonant excitation is vibrationally excited, and this gives rise to an increasing transfer rate with increasing sample temperature.     

Resonance energy transfer from a fluorescent dye to a metal nanoparticle

A quantum mechanical theory of the rate of excitation energy transfer from a fluorescent dye molecule to the surface plasmonic modes of a spherical metal nanoparticle is presented. The theory predicts the distance dependence of the transfer rate to vary as 1/d(sigma), with sigma=3-4 at intermediate distances, in partial agreement with the recent experimental results. F?rster's 1/d(6) dependence is recovered at large separations. The predicted rate exhibits nontrivial nanoparticle size dependence, ultimately going over to an asymptotic, a(3) size dependence. Unlike in conventional fluorescence resonance energy transfer, the orientational factor is found to vary between 1 and 4.     

Long distance energy transfer in a polymer matrix doped with a perylene dye

Exciton migration over long distances is a key issue for various applications in organic electronics. We investigate a disordered material system which has the potential for long exciton diffusion lengths in combination with a high versatility. The perylene bisimide dye Perylene Red is incorporated in a polymer matrix with a high concentration. The dye molecules represent active sites with a narrow energy distribution for the electronically excited states. Excitons can be efficiently exchanged between them by F?rster resonance energy transfer (FRET). The narrow energy distribution reduces drastically the trapping probability of the excitons compared to polymers and allows for long transfer distances. To characterize the mobility of the excitons and their diffusion length the dye Oxazine 1 is added as an acceptor in low concentration and the transfer probability to the acceptor is determined by measuring the reduction of Perylene Red fluorescence. The quenched quantum yield is measured for dye concentrations varying from 0.05?M to 0.15 M for Perylene Red and from 0.3 mM to 3 mM for Oxazine 1. The experimental results are compared to a model which assumes that excitons can diffuse through the material by FRET between Perylene Red sites and are trapped at an acceptor with a final hetero FRET step. We find a quite good match between theory and experiment though the observed diffusion constant is about two times smaller than the calculated one. The exciton diffusion length extracted from the data is 30 nm for a Perylene Red concentration of 0.1 M and demonstrates that long distance energy transfer is possible in this disordered material system.     

Ultrafast dynamics of acetylacetone (2,4-pentanedione) in the S2 state

The dynamics of the enolic form of acetylacetone (E-AcAc) was investigated using a femtosecond pump-probe experiment. The pump at 266 nm excited E-AcAc in the first bright state, S2(pi pi*). The resulting dynamics was probed by multiphoton ionization at 800 nm. It was investigated for 80 ps on the S2(pi pi*) and S1(n pi*) potential energy surfaces. An important step is the transfer from S2 to S1 that occurs with a time constant of 1.4 +/- 0.2 ps. Before, the system had left the excitation region in 70 +/- 10 fs. An intermediate step was identified when E-AcAc traveled on the S2 surface. Likely, it corresponds to an accidental resonance in the detection scheme that is met along this path. More importantly, some clues are given that an intramolecular vibrational energy relaxation is observed, which transfers excess vibrational energy from the enolic group O-H to the other modes of the molecule. The present multistep evolution of excited E-AcAc probably also describes, at least qualitatively, the dynamics of other electronically excited beta-diketones.     

Graphene as a quencher of electronic excited states of photochemical probes

Graphene sheets quench the singlet and triplet excited states of a series of six photochemical probes including pyrene, acridine orange, tris(2,2?-bipyridyl)ruthenium(II) dichloride, methylene blue, meso-tetrakis(phenylsulphonate)porphyrin, and 5,10,15,20-tetraphenyl-21H,28H-porphine zinc. It was found that Stern-Volmer fluorescence quenching can fit to one or two different quenching regimes depending on the probe. In addition, the quenching can be either static or dynamic depending on the fluorophore. The occurrence of several quenching regimes has been interpreted considering that quenching arises from the crowding of the fluorophore on both graphene faces, or site isolation on the graphene sheets. Laser flash photolysis has shown that the triplet lifetime of the probes generally decreases due to graphene quenching and that no new transients appear except in the case of methylene blue, where a new absorption spectrum characterized by a continuous absorption band is observed and attributed to graphene radical ion. This spectroscopic evidence suggests that the most general quenching mechanism is energy transfer from the singlet or triplet excited state of the dye to graphene. This raises the issue of determining the energy of the electronic excited states of graphene.     

Energy Transfer between Flavin and Cytochrome c

Energy transfer between photoexcited flavin and cytochrome c has been investigated in order to estimate intermolecular forces between flavin and cytochrome c. The quenching of the fluorescence of flavin by cytochrome c excited at 372 nm was found to be much greater than that excited at 465 nm. This dependence of the quenching on the exciting wavelength is considered to be due to the “prerelaxational” fast energy transfer. From the analysis of the quenching of the fluorescence of FMN and lumiflavin by cytochrome c excited at 465 nm, it was concluded that 1) the quenching is mainly controlled by resonance energy transfer, and 2) the heterogeneous dispersion state of molecules due to electrostatic forces makes the critical transfer distance, R ₀, of the resonance process longer than the real distance. For the quenching of the fluorescence of flavodoxin by cytochrome c, it was found that complex formation is a dominant process and is controlled to a great extent by electrostatic forces. Furthermore, fluorescence decay curves were measured by a single-photon counting method in order to estimate the dynamic processes of flavin fluorescence. The results also showed that the resonance process exists in the energy transfer between flavin and cytochrome c.     

Multimodal coupling of optical transitions and plasmonic oscillations in rhodamine B modified gold nanoparticles

The optical properties of a photoluminescent dye rhodamine B (RhB) interacting with gold nanoparticles (AuNP) have been investigated using plasmonic absorbance, fluorescence, and resonance elastic light scattering (RELS) spectroscopy. We have found that these interactions result in a multimodal coupling that influence optical transitions in RhB. In absorbance measurements, we have observed for the first time the coupling resulting in strong screening of RhB π-π* transitions, likely caused by a contact adsorption of RhB on a conductive surface of AuNP. The nanoparticles quench also very efficiently the RhB fluorescence. We have determined that the static quenching mechanism with a non-F?rster fluorescence resonance energy transfer (FRET) from RhB molecules to AuNP is involved. The Stern-Volmer dependence F(0)/F = f(Q) shows an upward deviation from linearity, attributed to the ultra-high quenching efficiency of AuNP leading to the new extended Stern-Volmer model. A sharp RELS peak of RhB alone (λ(max) = 566 nm) has been observed for the first time and attributed to the resonance fluorescence and enhanced scattering. This peak is completely quenched in the presence of AuNP(22nm). Our quantum mechanical calculations confirm that the distance between AuNP surface and conjugated π-electron system in RhB is well within the range of plasmonic fields extending from AuNP. The optical transition coupling to plasmonic oscillations and the efficient energy transfer due to the interactions of fluorescent dyes with nanoparticles are important for biophysical studies of life processes and applications in nanomedicine.     

Photoinduced electron transfer in hydrogen bonded donor--acceptor systems. Free energy and distance dependence studies and an analysis of the role of diffusion.

The free energy dependence of electron transfer in a few small-molecule donor--acceptor systems having hydrogen-bonding appendages was studied to evaluate the role of diffusion in masking the inverted region in bimolecular PET reactions. A small fraction of the probe molecules associate and this led to the simultaneous observation of unimolecular and diffusion-mediated quenching of the probe fluorescence. Free energy dependence studies showed that the unimolecular electron transfer obeys Marcus behavior and the diffusion-mediated electron transfer obeys Rehm--Weller behavior. The absence of an inverted region in bimolecular PET reactions is thus attributed to diffusion. The results of the free energy dependence studies suggest that distance dependence of electron transfer plays a role in masking the inverted region. To ascertain this aspect we have carried out a study of the distance dependence of electron transfer in the hydrogen-bonded donor--acceptor systems. For a system in the normal region an exponential rate decrease was observed. For a system in the inverted region it was observed that the rate depends very feebly on distance. Thus distance dependence studies did not confirm the prediction of enhanced rates at larger distances in the inverted region.     

Ultrafast Electron Transfer Kinetics of Graphene Grown by Chemical Vapor Deposition

High electrochemical reactivity is required for various energy and sensing applications of graphene grown by chemical vapor deposition (CVD). Herein, we report that heterogeneous electron transfer can be remarkably fast at CVD‐grown graphene electrodes that are fabricated without using the conventional poly(methyl methacrylate) (PMMA) for graphene transfer from a growth substrate. We use nanogap voltammetry based on scanning electrochemical microscopy to obtain very high standard rate constants k⁰≥25 cm s^?1 for ferrocenemethanol oxidation at polystyrene‐supported graphene. The rate constants are at least 2–3 orders of magnitude higher than those at PMMA‐transferred graphene, which demonstrates an anomalously weak dependence of electron‐transfer rates on the potential. Slow kinetics at PMMA‐transferred graphene is attributed to the presence of residual PMMA. This unprecedentedly high reactivity of PMMA‐free CVD‐grown graphene electrodes is fundamentally and practically important.     

Factors affecting the TMPTA radical polymerization photoinitiated by phenyltrialkylborates paired with tri-cationic hemicyanine dye. Kinetic studies

This article introduces tri-cationic hemicyanine dye employed as a visible-light photoinitiator of acrylic monomers polymerization. This dye, in combination with borate anions, was found to be a very effective photoinitiating system. The kinetics of trimethylolpropane triacrylate polymerization was studied by a microcalorimetric method. The photoredox pair concentration, the co-initiator structure as well as the light intensity strongly affected the progress of the polymerization, leading, for example, to an increase in the polymerization rate and quantum yield of the process. The efficiency of these photoinitiators was discussed on the basis of the free energy change for electron transfer from a borate anion to an excited hemicyanine dye cation. The ?G _el values were estimated for photoredox pairs containing a series of phenyltrialkylborate anions and one styrylpyridinium dye cation. The relationship between the rate of polymerization and the free energy of activation for electron transfer reaction gives the dependence predicted by the classical theory of electron transfer. The photoinitiating abilities of the selected novel photoredox pairs (BPB61, BPB7, BPB8, and BPB9) are comparable with the photoinitiating efficiency of commercially available photoinitiators.     

Quantitative determination of 1sigma(g)+ and 1delta(g) singlet oxygen in solvents of very different polarity. General energy gap law for rate constants of electronic energy transfer to and from O2 in the absence of charge transfer interactions

The quenching of excited triplet states of sufficient energy by O2 leads to O2(1sigma(g)+) and O2(1delta(g)) singlet oxygen and O2(3sigma(g)-) ground-state oxygen as well. The present work investigates the question whether in the absence of charge transfer (CT) interactions between triplet sensitizer and O2 the rate constants of formation of the three different O2 product states follow a generally valid energy gap law. For that purpose, lifetimes of the upper excited O2(1sigma(g)+) have been determined in a mixture of 7 vol % benzene in carbon tetrachloride, in chloroform, and in perdeuterated acetonitrile. They amount to 1.86, 1.40, and 0.58 ns, respectively. Furthermore, rate constants of O2(1sigma(g)+), O2(1delta(g)), and O2(3sigma(g)-) formation have been measured in these three solvents for five pi pi* triplet sensitizers with negligible CT interactions. The rate constants are independent of solvent polarity. After normalization for the multiplicity of the respective O2 product state, the rate constants follow a common dependence on the excess energies of the respective product channels. This empirical energy gap relation describes also quantitatively the rate constants of quenching of O2(1delta(g)) by 28 carotenoids. Therefore, it represents in the absence of CT interactions a generally valid energy gap law for the rate constants of electronic energy transfer to and from O2.     

Organically modified silica nanoparticles co-encapsulating photosensitizing drug and aggregation-enhanced two-photon absorbing fluorescent dye aggregates for two-photon photodynamic therapy

We report energy-transferring organically modified silica nanoparticles for two-photon photodynamic therapy. These nanoparticles co-encapsulate two-photon fluorescent dye nanoaggregates as an energy up-converting donor and a photosensitizing PDT drug as an acceptor. They combine two features: (i) aggregation-enhanced two-photon absorption and emission properties of a novel two-photon dye and (ii) nanoscopic fluorescence resonance energy transfer between this nanoaggregate and a photosensitizer, 2-devinyl-2-(1-hexyloxyethyl)pyropheophorbide. Stable aqueous dispersions of the co-encapsulating nanoparticles (diameter < or = 30 nm) have been prepared in the nonpolar interior of micelles by coprecipitating an organically modified silica sol with the photosensitizer and an excess amount of the two-photon dye which forms fluorescent aggregates by phase separation from the particle matrix. Using a multidisciplinary nanophotonic approach, we show: (i) indirect excitation of the photosensitizer through efficient two-photon excited intraparticle energy transfer from the dye aggregates in the intracellular environment of tumor cells and (ii) generation of singlet oxygen and in vitro cytotoxic effect in tumor cells by photosensitization under two-photon irradiation.     

Resonance energy transfer from a fluorescent dye molecule to plasmon and electron-hole excitations of a metal nanoparticle

The authors study the distance dependence of the rate of electronic excitation energy transfer from a dye molecule to a metal nanoparticle. Using the spherical jellium model, they evaluate the rates corresponding to the excitation of l=1, 2, and 3 modes of the nanoparticle. The calculation takes into account both the electron-hole pair and the plasmon excitations of the nanoparticle. The rate follows conventional R(-6) dependence at large distances while small deviations from this behavior are observed at shorter distances. Within the framework of the jellium model, it is not possible to attribute the experimentally observed d(-4) dependence of the rate to energy transfer to plasmons or electron-hole pair excitations.     

Effect of Delocalization and Rigidity in the Acceptor Ligand on MLCT Excited-State Decay

In its most simple form, the energy gap law for excited-state nonradiative decay predicts a linear dependence of ln k(nr) on the ground- to excited-state energy gap, where k(nr) is the rate constant for nonradiative decay. At this level of approximation, the energy gap law has been successfully applied to nonradiative decay in a wide array of MLCT excited states of polypyridyl complexes of Re(I), Ru(II), and Os(II). This relationship also predicts a dependence of k(nr) on the structural characteristics of the acceptor ligand. We report here a brief survey of the literature which suggests that such effects exist and have their origin in the extent of delocalization of the excited electron in the ligand pi framework and on acceptor ligand rigidity.     

Single-molecule four-color FRET visualizes energy-transfer paths on DNA origami

Fluorescence resonance energy transfer (FRET) represents a mechanism to transport light energy at the nanoscale, as exemplified by nature's light-harvesting complexes. Here we used DNA origami to arrange fluorophores that transport excited-state energy from an input dye to an output dye. We demonstrate that energy-transfer paths can be controlled on the single-molecule level by the presence of a "jumper" dye that directs the excited-state energy either to a red or to an IR output dye. We used single-molecule four-color FRET with alternating laser excitation to sort subpopulations and to visualize the control of energy transfer.