Les réactions 136Xe + p et 136Xe + 12C à 1 GeV par nucléon d’énergie cinétique du projectile dans le centre de masse ont été étudiées en cinématique inverse à l’aide du dispositif expérimental SPALADIN, installé auprès de l’accélérateur d’ions lourds de GSI. Ma thèse décrit l’analyse de ces collisions réalisées au printemps 2009. La détection en coïncidence des fragments de l’état final (résidu du projectile, neutrons et fragments légers chargés) avec une grande efficacité géométrique est obtenue par la combinaison de la cinématique inverse, d’un aimant dipolaire de grande ouverture physique et de l’utilisation de grands détecteurs. Ces coïncidences, mesurées événement par événement, nous ont permis de sélectionner, indépendamment du modèle de désexcitation, le pré-fragment, noyau excité issu de la cascade intranucléaire en fonction de son énergie d’excitation. Ainsi, nous avons pu étudier l’évolution du mécanisme de désexcitation (par exemple, l’évaporation de particules légères, la cassure binaire asymétrique ou la fragmentation multiple simultanée) en fonction de l’énergie d’excitation du pré-fragment. Les données de la réaction 136Xe + p sont comparées principalement à trois modèles de désexcitation (SMM, GEMINI++ et ABLA07) couplés au code de cascade intranucléaire INCL4. Si ces modèles semblent décrire globalement les observables de notre expérience, des désaccords significatifs sont apparus notamment en ce qui concerne la production des fragments de masse intermédiaire (IMF). La comparaison des données 136Xe + 12C avec celles de la réaction 136Xe + p fait apparaître une grande similitude dans la désexcitation des pré-fragments qui laisse entrevoir que la cascade intranucléaire mène, dans les deux cibles, aux mêmes types de pré-fragments sur la plage d’énergie d’excitation commune aux deux réactions (0 à 4 MeV par nucléon). Le régime d’excitation au-dessus de 4 MeV par nucléon, accessible uniquement pour la réaction 136Xe + 12C, montre une différence qualitative dans la désexcitation du pré-fragment, avec notamment une production beaucoup plus importante d’IMF, avec des multiplicités élevées par événement, qui croît avec l’énergie d’excitation. / The collision of 136Xe with the proton and with 12C at 1 GeV per nucleon of projectile kinetic energy in the centre of mass has been studied in inverse kinematics using the SPALADIN experimental setup at the GSI facility. This manuscript describes the analysis of these collisions realized in spring 2009. The detection in coincidence of the final state fragments (projectile residues, neutrons and light charged fragments) with a large geometrical efficiency is provided by the inverse kinematics combined with a large aperture dipole magnet and large detectors. Such a coincidence, measured on an event basis, allows selecting, in a model-independent way, the prefragment, the excited nuclear system formed after the intranuclear cascade as a function of its excitation energy. Hence, we were able to study the evolution of the prefragment deexcitation mechanism (evaporation of light particles, asymmetric binary decay, multiple fragmentation…) as a function of its excitation energy. The data of the 136Xe + p reaction have been compared mainly to three deexcitation models (SMM, GEMINI++ and ABLA07) coupled to the intranuclear cascade code INCL4. Despite the relatively good and global agreement between these models and our data, significant discrepancies appeared concerning in particular the production of intermediate mass fragments (IMF). Comparison between the 136Xe + 12C and the 136Xe + p data exhibits an important similarity in the deexcitation of the pre-fragments. This suggests that the nuclear cascade leads, for both targets, to similar prefragment types in the range of excitation energy (0 to 4 MeV per nucleon) common to both reactions. Higher excitation energies, reached only in the 136Xe + 12C reaction, show a qualitative difference in the deexcitation of the pre-fragment, with much higher multiplicities of IMF per event, increasing with the excitation energy.

abstract: Photosystem I (PSI) is a multi-subunit, pigment-protein complex that catalyzes light-driven electron transfer (ET) in its bi-branched reaction center (RC). Recently it was suggested that the initial charge separation (CS) event can take place independently within each ec2/ec3 chlorophyll pair. In order to improve our understanding of this phenomenon, we have generated new mutations in the PsaA and PsaB subunits near the electron transfer cofactor 2 (ec2 chlorophyll). PsaA-Asn604 accepts a hydrogen bond from the water molecule that is the axial ligand of ec2B and the case is similar for PsaB-Asn591 and ec2A. The second set of targeted sites was PsaA-Ala684 and PsaB-Ala664, whose methyl groups are present near ec2A and ec2B, respectively. We generated a number of mutants by targeting the selected protein residues. These mutations were expected to alter the energetics of the primary charge separation event. The PsaA-A684N mutants exhibited increased ET on the B-branch as compared to the A-branch in both in vivo and in vitro conditions. The transient electron paramagnetic resonance (EPR) spectroscopy revealed the formation of increased B-side radical pair (RP) at ambient and cryogenic temperatures. The ultrafast transient absorption spectroscopy and fluorescence decay measurement of the PsaA-A684N and PsaB-A664N showed a slight deceleration of energy trapping. Thus making mutations near ec2 on each branch resulted into modulation of the charge separation process. In the second set of mutants, where ec2 cofactor was target by substitution of PsaA-Asn604 or PsaB-Asn591 to other amino acids, a drop in energy trapping was observed. The quantum yield of CS decreases in Asn to Leu and His mutants on the respective branch. The P700 triplet state was not observed at room and cryogenic temperature for these mutants, nor was a rapid decay of P700+ in the nanosecond timescale, indicating that the mutations do not cause a blockage of electron transfer from the ec3 Chl. Time-resolved fluorescence results showed a decrease in the lifetime of the energy trapping. We interpret this decrease in lifetime as a new channel of excitation energy decay, in which the untrapped energy dissipates as heat through a fast internal conversion process. Thus, a variety of spectroscopic measurements of PSI with point mutations near the ec2 cofactor further support that the ec2 cofactor is involved in energy trapping process. / Dissertation/Thesis / Doctoral Dissertation Biochemistry 2014

abstract: The first chapter reviews three decades of artificial photosynthetic research conducted by the A. Moore, T. Moore, and D. Gust research group. Several carotenoid (Car) and tetrapyrrole containing molecules were synthesized and investigated for excitation energy transfer (EET), photoregulation, and photoprotective functions. These artificial photosynthetic compounds mimicked known processes and investigated proposed mechanisms in natural systems. This research leads to a greater understanding of photosynthesis and design concepts for organic based solar energy conversion devices. The second and third chapters analyze the triplet energy transfer in carotenoid containing dyads. Transient absorption, time-resolved FTIR and resonance Raman spectra revealed that in a 4-amide linked carotenophthalocyanine dyads the Car triplet state is shared across the larger conjugated system, which is similar to protein complexes in oxygenic photosynthetic organisms. In a carotenopurpurin dyad (CarPur) a methylene ester covalent bond prevents the purpurin (Pur) from influencing the Car triplet based on the transient absorption, time-resolved FTIR and resonance Raman spectra. Thus CarPur resembles the antenna proteins from anoxygenic photosynthetic bacteria. Additional examples of carotenoporphyrin dyads further demonstrates the need for orbital overlap for ultrafast triplet energy transfer and the formations of possible intramolecular charge transfer state. The fourth chapter studies a 4-amino phenyl carotenophthalocyanine and its model compounds using high temporal resolution transient absorption spectroscopy techniques. EET from the Car second excited (S2) state to the phthalocyanine (Pc) was determined to be 37% and a coupled hot ground state (S*)/Pc excited state spectrum was observed. Excitation of the tetrapyrrole portion of the dyad did not yield any kinetic differences, but there was an S* signal during the excited states of the dyad. This demonstrates the EET and photoregulating properties of this artificial photosynthetic compound are similar to those of natural photosynthesis. The last chapter covers the synthesis of silicon Pc (SiPc) dyes and the methods for attaching them to gold nanoparticles and flat gold surfaces. SiPc attached to patterned gold surfaces had unperturbed fluorescence, however the selectivity for the gold was low, so alternative materials are under investigation to improve the dye's selectivity for the gold surface. / Dissertation/Thesis / Ph.D. Chemistry 2014

No abstract provided. / Thesis / Master of Science (MSc) / Scope and contents: The probability of fission as a function of primary fragment velocities has been obtained by removing the neutron emission and instrumental dispersions from the velocities determined by Stein with time-of-flight techniques for the thermal neutron fission of u235. Each velocity was increased by 0.69% to make the average kinetic energy per fission agree with the calorimetric value of 167.1 Mev. Excitation energy distributions were obtained by using the primary fragment masses given by Cameron and assuming that the most probable charge distribution for a given mass ratio i s that which leads to the greatest energy release. Evaporation theory was used to determine the number of prompt neutrons emitted. When the excitation energy is divided equally between the fragments and a nuclear temperature of 0.59 Mev is used, the average number of neutrons emitted is 2.95 per fission.

A key component of natural photosynthesis are the antenna chromophores (chlorophylls and carotenoids) that capture solar energy and direct it towards the reaction centers of photosystems I and II. Highlighted by highly-ordered crystal structures and synthetic tunability via crystal engineering, metal–organic frameworks (MOFs) have the potential to mimic the natural photosynthetic systems in terms of the efficiency and directionality of energy transfer. Owing to their larger surface areas, MOFs have large absorption cross sections, which amplifies the rate of photon collection. Furthermore, MOFs can be constructed using analogues of chlorophyll and carotenoids that can participate in long-range energy transfer. Herein, we aimed to design photoactive MOFs that can execute one of the critical steps involved in photosynthesis - photon collection and subsequent energy transfer. The influence of spatial arrangement of chromophores on the efficiency and directionality of excitation energy transfer (EET) was investigated in a series of mixed-ligand pyrene- and porphyrin-based MOFs. Due to the significant overlap between the emission spectrum of 1,3,6,8-tetrakis(p-benzoic acid)pyrene (TBAPy) and the absorption spectrum of meso-tetrakis(4-carboxyphenyl)porphyrin (TCPP), the co-assembly of these two ligands in a MOF should enable facile energy transfer. Bearing this in mind, three TBAPy-based MOFs with markedly different network topologies (ROD-7, NU-901, and NU-1000) were chosen and a small number of TCPP units were incorporated in their backbone. To gain insight into the photophysical properties of mixed-ligand MOFs, we conducted time-resolved and steady-state fluorescence measurements on them. Stern-Volmer analysis was performed on the fluorescence lifetime data of mixed-ligand MOFs to determine the quenching constants. The quenching constant values for ROD-7, NU-901, NU-1000, and TBAPy solution were found to be 15.03 ± 0.82 M-1, 10.25 ± 0.99 M-1, 8.16 ± 0.41 M-1, and 3.35 ± 0.30 respectively. In addition, the ratio of the fluorescence intensities of TCPP and TBAPy was used to calculate the EET efficiencies in each of the three MOFs. EET efficiencies were in the following order: ROD-7 > NU-901 > NU-1000 > TBAPy-solution. Based on the trends observed for quenching constants and EET efficiencies, two conclusions were drawn: (1) the ligand-to-ligand energy transfer mechanism in MOFs outperforms the diffusion-controlled mechanism in solution phase, (2) energy transfer in MOFs is influenced by their structural parameters and spectral overlap integrals. The enhanced EET efficiency in ROD-7 is attributed to shorter interchromophoric distance, larger orientation factor, and larger spectral overlap integral. Directionality of energy transfer in these MOFs was assessed by calculating excitonic couplings between neighboring TBAPy linkers using the atomic transition charges approach. Rate constants of EET (kEET) along different directions were determined from the excitonic couplings. Based on the kEET values, ROD-7 is expected to demonstrate highly anisotropic EET along the stacking direction. In order to explore the mechanistic aspects of EET in porphyrin-based MOFs, we studied the energy transfer characteristics of PCN-223, a zirconium-based MOF containing TCPP ligands. After performing structural characterization, the photophysical properties of PCN-223 and free TCPP were investigated using steady state and time-resolved spectroscopy. pH-dependent fluorescence quenching experiments were performed on both the MOF and ligand. Stern-Volmer analysis of quenching data revealed that the quenching rate constants for PCN-223 and TCPP were 8.06 ± 1011 M-1s-1 and 2.71 ± 1010 M-1s-1 respectively. The quenching rate constant for PCN-223 is, therefore, an order of magnitude larger than that for TCPP. Additionally, PCN-223 demonstrated a substantially higher extent of quenching (q = 93%) as compared to free TCPP solution (q = 51%), at similar concentrations of quencher. The higher extent of quenching in MOF is attributed to energy transfer from neutral TCPP linkers to N-protonated TCPP linkers. Using the Förster energy transfer model, the rate constant of EET in PCN-223 was calculated. The magnitude of rate constant was in good agreement with the kEET values reported for other porphyrin-based MOFs. Nanosecond transient absorption measurements on PCN-223 revealed the presence of a long-lived triplet state (extending beyond 200 μs) that exhibits the characteristic features of a TCPP-based triplet state. The lifetime of MOF is shorter than that of free ligand, which may be attributed to triplet-triplet energy transfer in the MOF. Lastly, femtosecond transient absorption spectroscopy was employed to study the ultrafast photophysical processes taking place in TCPP and PCN-223. Kinetic analysis of the femtosecond transient absorption data of TCPP and PCN-223 showed the presence of three distinct time components that correspond to: (a) solvent-induced vibrational reorganization of excitation energy, (b) vibrational cooling, and (c) fluorescence. Materials that allow control over the directionality of energy transfer are highly desirable. Core-shell nanocomposites have recently emerged as promising candidates for achieving long-distance, directional energy transfer. For our project, we aim to employ UiO-67-on-PCN‐222 composites as model systems to explore the possibility of achieving directional energy transfer in MOF-based core-shell structures. The core–shell composites were synthesized by following a previously published procedure. Appropriate amounts of Ruthenium(II) tris(5,5′-dicarboxy-2,2′-bipyridine), RuDCBPY, were doped in the shell layer to produce a series of Ru-UiO-67-on-PCN‐222 composites with varying RuDCBPY loadings (CS-1, CS-2, and CS-3). The RuDCBPY-doped core–shell composites were characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM) imaging, Nitrogen adsorption-desorption isotherms, and diffuse reflectance spectroscopy. Efforts are currently underway to quantify RuDCBPY loadings in CS-1, CS-2, and CS-3. After completing structural characterization, the photophysical properties of CS-1, CS-2, and CS-3 will be investigated with the help of time-resolved and steady-state fluorescence spectroscopy. / Doctor of Philosophy / The pigment−protein complexes in natural photosynthetic units (also known as light harvesting antennas) efficiently capture solar energy and transfer this energy to reaction centers that carry out water splitting reactions. The collective chromophoric behavior of antennas can be replicated by metal-organic frameworks (MOFs). MOFs are crystalline, self-assembled materials composed of metal clusters connected by organic molecules. In this dissertation, we study the factors that govern the energy transfer and light harvesting capabilities of MOFs. In chapter 2, we examined the role of 3D structure of MOFs in energy transfer. In chapter 3, we investigated the influence of pH and temperature on the photophysical properties of MOFs. In chapter 4, we explored the possibility of energy transfer in novel MOF-on-MOF composites. This work is intended to pave the way for the construction of highly efficient MOF-based materials that can serve as the light harvesting and energy-transfer components in solar energy conversion devices.

This thesis consists of two parts and nine chapters. The first part (Part I) presents theoretical studies on non-radiative mode of excitation energy transfer (EET) in donor-acceptor (D-A) systems involving metal nanoparticles. Part I contains four chapters and describes EET in following different D-A systems: (i) dye and a spherical metal nanoparticle of different sizes, (ii) two spherical metal nanoparticles, and (iii) two prolate shaped metal nanoparticles at different relative orientations. Part II provides a detailed study on the origin of photochemical funneling of excitation energy in conjugated polymers like poly-[phenylenevinylene] (PPV) and consists of three chapters. The ninth chapter provides a concluding note. The thesis begins with a basic introduction on Forster resonance energy transfer(FRET), presented in chapter 1. This chapter provides a detail derivation of Forster’s rate expression for a non-radiative process of EET from a donor to an acceptor molecule and discusses the limitations of Forster theory. The chapter highlights the huge success of FRET technique in understanding biological processes assisted by changes in conformations of biopolymers under conditions where Frster theory is valid. The chapter also discusses practical limitations of FRET technique such as use of pre-averaged value of orientation factor and photobleaching of dye molecules. Part I starts with chapter 2 which explains the advantages of using metal nanoparticles over dye molecules in D-A systems. The chapter discusses recent experimental re-ports of excitation energy transfer to nanoparticles, now commonly referred to as nanoparticle surface energy transfer (NSET). Theories describing the process of EET from a dye molecule (dye molecule is assumed to be a point dipole) to a planar metallic surface are discussed. In the case of energy transfer from a donor dye molecule to a planar metallic surface, the distance dependence of the rate of EET is found to vary as 1/d4 where dis a distance from the center of a dye molecule to the metallic surface. This is unlike conven-tional FRET where rate of EET follows 1/R6 distance dependence with R as a distance between the centers of D and A. Also, a recent experimental study by Yun et al [J. Am. Chem. Soc. 127, 3115 (2005)] on energy transfer from a dye molecule to a spherical gold nanoparticle reports that the rate of EET follows 1/d4 distance dependence. The remaining chapters of this part focus on understanding this deviation from the Forster theory in different D-A systems. Chapter 3 describes quantized electro-hydrodynamic approach used to model the plasmonic excitations in metal nanoparticles. The optical absorption frequencies of nanoparticles computed here are subsequently used in chapters 4 and 5 for the calculation of the rate of EET. The chapter discusses the merits and de-merits of electro-hydrodynamic approach in comparison to other available techniques. The electro-hydrodynamic method of calculating the absorption frequencies provide a physically appealing, mathematically simple and numerically tractable approach to the problem and is also at the same time, semi-quantitatively reliable. The optical frequencies obtained as a function of size and aspect ratio of metal nanoparticles are found to be in good agreement with physical predictions. Chapter 4 studies the distance dependence of rate of EET for a D-A system similar to one studied by Yun et al [J. Am. Chem. Soc. 127, 3115 (2005)]. The chapter contains the relevant derivations of the quantities required for computing the interaction matrix elements. The dependence of the rate of EET on R is found surprisingly to be in agreement with Forster theory even at intermediate distances compared to the size of spherical nanoparticles (a). However, the dependence of rate of EET on d is found to vary as 1/dσwith σ=3 - 4 at intermediate distances which is in good agreement with the experimental results of Yun et al. At large values of d, the distance dependence of rate is found to vary as 1/d6 . The chapter discusses the physical basis behind these results. The theory predicts a non-trivial dependence of rate on the size of a nanoparticle which ultimately attains the asymptotic a3 size dependence. The rate of EET is also studied for different orientations of dye molecule. Chapter 5 studies surface plasmon mediated EET between two metal nanoparticles. The rate of EET between two prolate and spherical shaped silver nanoparticles is studied as a function of Rand d. d, in present chapter denotes surface-to-surface separation distance between two nanoparticles. In case of EET between two non-spherical nanoparticles, even at separations larger than the size of the nanoparticle, a significant deviation from 1/R6 dependence is obtained. However, 1/R6 distance dependence of EET rate is found to be robust for spherical nanoparticles over an entire range of separations. The deviation of rate from 1/R6 distance dependence becomes more pronounced with in-crease in the aspect ratio of the nanoparticle. The relative orientation of the nanoparticles is found to markedly influence the R-dependence of EET rate. Interestingly, the relative orientation of nanoparticles effect the d-distance dependence of the rate to a lesser extend in comparison to the R-dependence of the rate. Therefore, we predict that for non-spherical nanoparticles studying EET rate as a function of will provide more conclusive results. The chapter also discusses the size dependence of rate of EET for this particular D-A system. In Part II, excitation energy transfer (EET) in a conjugated polymer is studied. To start with, chapter 6 provides a brief introduction to photophysics of conjugated polymers. The chapter discusses the nature of photoexcitations in these systems and stresses on the influence of polymer’s morphology on the optical properties of conjugated polymers. Chapter 7 describes the theory used for modeling conjugated polymer chain. A polymer chain consists of number of spectroscopic units (chromophores) of varying lengths. The average length of chromophores in conjugated polymer depends on defect concentration. In the present study we treat an excitation generated on each chromophore within “particle-in-a-box” formalism but one that takes into account the electron-hole interactions. The transition dipole moments and the radiative rates are computed for different lengths of chromophores with parameters appropriate for PPV chain. These quantities are used in chapter 8 for calculating the absorption and emission spectra of conjugated polymer chains at different defect concentrations. The main aim of Chapter 8 is to understand the origin of photochemical funneling of excitation energy in conjugated polymers. PPV chain is modeled as a polymer with the length distribution of chromophores given either by a Gaussian or by a Poissonian distribution. We observe that the Poissonian distribution of length segments explains the optical spectra of PPV rather well than the Gaussian distribution. The Pauli’s master equation is employed to describe the excitation energy transfer among different chromophores. The rate of energy transfer is assumed to be given here, as a first approximation, by the well-known Forster expression. The observed excitation population dynamics confirm the photochemical funneling of excitation energy from shorter to longer chromophores of the polymer chain. The calculations show that even in steady state more than one type of chromophore contribute towards the emission spectrum. The observed difference between the calculated emission spectra at equilibrium and in steady state indicates the existence of local domains in a polymer chain within which the non-radiative excitation energy transfer from shorter to longer chromophores take place. These results are found to be in agreement with recent experimental reports. The concluding chapter 9 gives a brief summary of the outcome of the thesis and ends up with suggestion of a few future problems which in current scenario are of great interest.

In this work, the Collision Induced Dissociation under Energy Control method was extended to study the fragmentation of gas-phase biomolecules adenine (H5C5N5) and porphyrin FeTPPCl (C44H28N4FeCl). The population distribution for each dissociation channel has been experimentally determined as a function of the excitation energy of the parent molecular ions at a well-determined initial charge state. In collisions between Cl+ and adenine (Ade) at 3keV, the fragmentation pattern of Ade2+ is dominated by the loss of H2CN+ and the successive emission of HCN. The energy distribution of the parent dications confirms the successive emission dynamics. A specific decay channel is observed, i.e., the emission of a charged H2CN+ followed by the emission of HC2N2. In Kr8+-FeTPPCl collisions at 80keV, parent ions FeTPPCl1+,2+,3+ are observed, along with the corresponding decay patterns. It is found that in the first step the dominant low-energy-cost decay channel is the emission of Cl0 independent of the initial charge state of FeTPPClr+ (r=1-3). For the resulted dication FeTPP2+, the dominant fragmentation channel is the neutral evaporation; for the trication however, the dominant fragmentation channel is the asymmetrical fission. In the case of H+ and F+ impact at 3keV, due to the different reaction windows opened in the two collision systems, different fragmentation patterns are observed. Furthermore, nH2 loss processes are observed. Additionally, the production yield of the negative ion emerged in F2+-Ade collision at 30keV is measured to be about 1% using a new experimental approach.

No description available.

Les performances des techniques de bioimagerie et de biodétection peuvent être améliorées grâce aux nanoparticules fluorescentes (NPs) permettant un transfert d’énergie résonante de type Förster (FRET) efficace. Le but de mon projet de thèse est le développement de NPs polymériques brillantes et ultrastables encapsulant des fluorophores, capables de produire un FRET au-delà du rayon de Förster. Il a été montré que les groupements encombrés sont essentiels pour minimiser l’auto-extinction et le blanchiment des fluorophores encapsulés. Par ailleurs, la matrice polymérique joue un rôle crucial dans le contrôle de l’effet collaboratif entre fluorophores du au transfert d’énergie d’excitation. Puis, en utilisant cet effet collaboratif entre fluorophores, nous avons conçu des NPs présentant une photocommutation efficace, ainsi qu'un phénomène de "light harvesting" très important. Enfin, de très petites NPs avec un FRET efficace à leur surface ont été élaborées et appliquées pour la détection ultra-sensible de protéines. Les résultats obtenus fournissent de nouvelles perspectives dans le développement des nanoparticules brillantes avec un transfert d'énergie efficace, ainsi que des nano-sondes pour la détection de molécules uniques. / Performance of biosensing and bioimaging techniques can be improved by fluorescent nanoparticles (NPs) capable of efficient Förster resonance energy transfer (FRET). The aim of my PhD project is to develop bright and photostable dye-loaded polymer NPs capable to undergo efficient FRET beyond the Förster radius. We showed that bulky groups are essential for minimizing self-quenching and bleaching of encapsulated dyes. Moreover, polymer matrix plays a crucial role in controlling the inter-fluorophore communication by excitation energy transfer. Then, by exploiting communication of dyes, we designed NPs exhibiting efficient photoswitching as well as giant light-harvesting. Finally, very small NPs with efficient FRET to their surface were developed and applied for ultra-sensitive molecule detection of proteins. The obtained results provide new insights in the development of bright nanoparticles with efficient energy transfer as well as nano-probes for single-molecule detection.

Electronic Excitation Energy Transfer is an important intermolecular photophysical process that can affect the excited state lifetime of a chromophore. A molecule in an electronically excited state can return to the ground state by radiative as well as non-radiative processes. During the excited state lifetime, if the chromophore (energy donor) finds a suitable species (energy acceptor) nearby with resonant energy levels, it can transfer the excitation energy to that species and return to the ground state. This process is called Electronic Excitation Energy Transfer. When the energy donor is fluorescent, the process is called Fluorescence Resonance Energy Transfer (FRET) [1]. FRET is a non-radiative process that affects the fluorescence intensity as well as the excited state lifetime of the donor. It occurs due to the electrostatic coulombic interaction between the transition charge densities of the donor and the acceptor. The rate of energy transfer can be evaluated using the Fermi golden rule of quantum mechanics [2]. When the donor and the acceptor are separated by distances that are much larger in comparison with the sizes of the donor and the acceptor, the interaction between them can be thought of as that between their transition dipoles. In such a case, the interaction between the donor and the acceptor is dipolar and the rate of energy transfer has an R−6 dependence, where R is the distance between the donor and the acceptor [3]. This dependence has first been suggested theoretically by Forster in 1947 [4] followed by the experimental verification by Stryer and Haugland [5]. Since then the process has been used as a spectroscopic ruler to study the conformational dynamics of biopolymers like DNA, RNA, proteins etc [6]. A variety of dye molecules have been explored for donors and acceptors in FRET and the range of distances that can be measured using FRET involving dyes is in the range 1 − 10 nm. When the distances between the donor and the acceptor are not much larger in comparison with their sizes, the dipolar approximation to the interaction is not a very good approximation, thereby leading to deviations from the traditional R-6 dependence. Such non-R-6dependencies are found for polymers, quantum wells, quantum wires etc [7–9]. The interest in such dependencies is due to the need for developing nanoscopic rulers that can measure distances well beyond 10 nm. The objective of our work has been to study energy transfer from fluorophores to various kinds of acceptors that have extended charge densities and understand the distance dependence of the rate of energy transfer [10]. We use the Fermi golden rule as the starting point and develop analytical models for evaluating the rate as a function of the distance between the donor and the acceptor. We study the process of energy transfer from fluorescent dye molecules that serve as energy donors to a variety of energy acceptors namely, graphene, doped graphene, single-walled carbon nanotubes and metal nanoparticles. We also study transfer from fluorophores to a semiconducting sheet and a semiconducting tube of electronic charge density. There have been experimental studies in the literature of the fluorescence quenching of dyes near single-walled carbon nanotubes [11–13]. But, there are no studies of the distance dependence of rate. Single-walled carbon nanotubes can be thought of as rolled up sheets of graphene. However, interestingly, there were no reports of fluorescence quenching by graphene at the time when we thought of this possibility. Therefore, we first study the process of energy transfer from a fluorophore, which is kept at a distance z above a layer of graphene to the electronic energy levels of graphene. We find that the long range behavior of the rate has an z -4 dependence on the distance [14, 15]. From our study of transfer from pyrene to graphene, we find that fluorescence quenching can be experimentally observed up to a distance of ~ 30 nm, which is quite large in comparison with the traditional FRET limit (10 nm). Recent experiments that have been performed after our theory was reported have in fact observed the fluorescence quenching of dyes near graphene. Further, the process has been found to be very useful in fabricating devices based on graphene [16], in eliminating fluorescence signals in resonance Raman spectroscopy [17] and in visualizing graphene based sheets using fluorescence quenching microscopy [18]. The process has also been found to be useful in quantitative DNA analysis [19, 20]. We study the transfer of an amount of energy hΩ from a dye molecule to doped graphene [21]. We consider the shift of the Fermi level from the K-point into the conduction band of graphene as a result of doping and evaluate the rate of transfer. We find a crossover of the distance dependence of the rate from z -4 to exponential as the Fermi level is increasingly shifted into the conduction band, with the crossover occurring at a shift of the Fermi level by an amount hΩ/2. We study the process of transfer of excitation energy from a fluorophore kept at a distance d away from the surface of a carbon nanotube to the electronic energy levels of the nanotube. We find both exponential and d−5 behavior of the rate [22]. For the case of metallic nanotubes, when the emission energy of the fluorophore is less than a threshold, the dependence is exponential. Otherwise, it is d−5 . For the case of semiconducting nanotubes, we find that the rate follows an exponential dependence if the amount of energy that is transferred can cause only the excitonic transition of the tube. However, if any other band gap transition is allowed, the rate follows a d−5 dependence. For the case of transfer from pyrene to a (6, 4) nanotube, we find that energy transfer is appreciable up to a distance of ~ 17 nm. We then study the process of energy transfer from a fluorophore to a semiconducting sheet of electronic charge density [10]. We find that the rate has an z-4 dependence. For the case of transfer to a semiconducting tube, we find that the rate has a d -5dependence. The dependencies are in agreement with those obtained for graphene and carbon nanotubes respectively. This shows that the asymptotic distance dependencies are a consequence of the dimensionality of the transition charge densities and are robust. Strouse et al. [23, 24] have studied the process of energy transfer from the dye fluorescein to a 1.4 nm diameter gold nanoparticle. Double-stranded DNA molecules of various lengths were used to fix the distances between the donor and the acceptor. The rate was found to have a d-4distance dependence. They refer to this process as Nanoparticle Surface Energy Transfer (NSET) and the range of distances that can be measured using NSET is more than double that of the traditional FRET experiments. However, theoretical studies that consider the transfer to the plasmonic modes of the nanoparticle find a predominant R-6 dependence [25]. We study the process of energy transfer from the dye fluorescein to a 1.4 nm diameter gold nanoparticle considering the excitation of plasmons as well as electron-hole pairs of the nanoparticle [26]. We find that the rate follows the usual Forster type R−6 distance dependence at large distances. But, at short distances, there are contributions of the form R−-n with n > 6. This is due to the quadrupolar and octupolar modes of excitation of the nanoparticle, the rates corresponding to which have R-8 and R−-10 dependencies respectively. Recent calculations using DFT also find similar deviations at short distances [27].