Calculated Energy Transfer Rates Research Articles

Intramolecular energy transfer and its influence on the overall quantum yields of Eu3+ and Tb3+ chelates with dimethyl(phenylsulfonyl)amidophosphate ligands

Lanthanide chelates with dimethyl(phenylsulfonyl)amidophosphate (labeled as HSP) and Lewis base ligands (bpy = 2,2;-bipyridine and phen = 1,10-phenanthroline) of formula Na[Ln(SP)4] (1Ln), [Ln(SP)3bpy] (2Ln); [Ln(SP)3phen] (3Ln) (Ln = Eu3+, Gd3+, Tb3+ and Lu3+) were obtained and characterized by the X-ray, photoluminescence spectroscopy at 293 and 77 K as well as by intrinsic (QLnLn) and overall (QLnL) luminescence quantum yields. These phosphors manifest a very strong emission after excitation in the UV range of the molecular singlet states (S1) and two of them have very high QLnL values (Eu3+ and Tb3+ chelates of the type 2Ln and 3Ln). The dynamics of the excited states are discussed based on the intramolecular energy transfer theory, considering the dipole–dipole, the dipole-multipole and the exchange mechanisms. From the calculated energy transfer rates, a rate equation model was constructed and, thus, the theoretical QLnL can be obtained. A good correlation between the experimentally determined and theoretically calculated QLnL values was achieved, with the triplet state (T1) playing a predominant role in the energy transfer process for Eu3+ compounds, while the sensitization for Tb3+ compounds is dominated by the energy transfer rates from the singlet state (S1).

Judd-Ofelt parameters and energy transfer rates of α-NaYF4:Eu3+– a theoretical and experimental study

We report the analysis of Europium (Eu3+) ion-doped NaYF4 thin films from an experimental and theoretical complementary point of view. The pristine and Eu3+ doped-NaYF4 thin films were obtained by electrochemical deposition in the cubic phase (α-NaYF4), which were fully characterized by X-ray diffraction, scanning electron microscopy, and photoluminescence techniques. The emission spectrum of α-NaYF4:Eu3+ exhibits two intense bands at 610 and 628 nm for 5D0 → 7F2 transition with an excitation energy source at 245 nm. The experimental emission spectrum of α-NaYF4:Eu3+ thin films suggests that the D4h could be the local point symmetry around Eu3+ because of the number of sublevels in 5D0 → 7F1,2 transitions. The LUMPAC software was used to calculate the excited states, Judd-Ofelt (J-O) parameters, and energy transfer rates (ETR) from ligand to Eu3+ semi-empirically, using the local point group symmetry proposed in this work. The obtained J-O parameters are Ω2 = 15.39 × 10−20 cm2, Ω4 = 2.14 × 10−20 cm2, and Ω6 = 0.1275 × 10−20 cm2, where Ω6 was calculated by the QDC method despite of 5D0→7F6 transition is not observed in the experimental emission spectrum. The calculated energy transfer rates give the energy transitions from ligand S1→T (singlet→triplet) to T→Eu3+. Finally, the analysis of molecular orbitals derived from time dependent-DFT calculations confirms that the electronic transfer occurs from F− → Eu3+ (from ligand to Eu3+).

Reheating in two-sector cosmology

We analyze reheating scenarios where a hidden sector is populated during reheating along with the sector containing the Standard Model. We numerically solve the Boltzmann equations describing perturbative reheating of the two sectors, including the full dependence on quantum statistics, and study how quantum statistical effects during reheating as well as the non-equilibrium inflaton-mediated energy transfer between the two sectors affects the temperature evolution of the two radiation baths. We obtain new power laws describing the temperature evolution of fermions and bosons when quantum statistics are important during reheating. We show that inflaton-mediated scattering is generically most important at radiation temperatures T ∼ Mϕ/4, and build on this observation to obtain analytic estimates for the temperature asymmetry produced by asymmetric reheating. We find that for reheating temperatures Trh ≪ Mϕ/4, classical perturbative reheating provides an excellent approximation to the final temperature asymmetry, while for Trh ≫ Mϕ/4, inflaton-mediated scattering dominates the population of the colder sector and thus the final temperature asymmetry. We additionally present new techniques to calculate energy transfer rates between two relativistic species at different temperatures.

Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots

AbstractIn the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

Modulating FRET in Organic–Inorganic Nanohybrids for Light Harvesting Applications

The energy transfer efficiencies of organic–inorganic nanohybrids comprised of two structurally similar squaraine dyes and CdSe nanoparticles were studied in detail and compared. Carbazole based unsymmetrical squaraine dyes (CTSQ-1 and CTSQ-2) having modified absorption characteristics were considered for modulating the effect of the overlap integral on energy transfer rate with the designed QDs. CTSQ-2 with ∼1.75 times higher molar extinction coefficient and 35 nm red-shift in absorption resulted in an ∼2.4 times faster energy transfer rate with QD. The calculated energy transfer rates (kT = 1.35 × 108 s–1 and 3.26 × 108 s–1 respectively for QD:CTSQ-1 and QD:CTSQ-2 nanohybrids) are at least one order of magnitude higher than both radiative (kr = 5.97 × 106 s–1) and nonradiative decay rate constants (knr = 1.89 × 107 s–1) of QDs yielding very high FRET efficiency. The Stern–Volmer analysis of the quenching data indicated mainly static interaction of dyes with the QDs thus suggesting formation of organic–i...

Quantifying the Lifetime of Triplet Energy Transfer Processes in Organic Chromophores: A Case Study of 4-(2-Naphthylmethyl)benzaldehyde.

We simulate the dynamics of triplet-triplet energy transfer in a donor-bridge-acceptor system [4-(2-naphthylmethyl)benzaldehyde] with surface hopping, using electronic energies, gradients, and derivative couplings that are calculated on the fly. Using Boys localization to diabatize electronic states, we calculate energy transfer rates that agree favorably with experiment. The atomistic nature of our dynamical investigation produces several unique insights into this energy transfer reaction including an approximation of the decoherence time for the energy transfer process and the observation that the reaction pathway passes through a conical intersection.

Bright and tunable up-conversion luminescence through cooperative energy transfer in Yb3+, Tb3+and Eu3+co-doped LaPO4nanocrystals

Lanthanum phosphate LaPO4 nanocrystals doped with Yb3+, Tb3+ and Eu3+ ions, were synthesised by a hydrothermal method followed by annealing at 900 °C. These materials exhibited bright and tunable up-conversion luminescence from green to red colour as the result of Tb3+ and Eu3+ ions emission. The structural and morphological properties of the products were analysed by X-ray diffraction (XRD) and transmission electron microscopy (TEM). The spectroscopic properties of LaPO4:Yb3+,Tb3+,Eu3+ nanocrystals were investigated using excitation and emission spectra. Also the luminescence decays were measured showing an unusually long rise time of the luminescence as a result of cooperative energy transfer mechanisms (CET) followed by energy migration. Calculated energy transfer rates and efficiencies showed the effectiveness of energy transfer between Yb3+, Tb3+ and Eu3+ ions.

Two-step quantum cutting efficiency in Pr3+-Yb3+codoped KY3F10

The efficiency of a two-step quantum cutting (QC) mechanism for solar downconversion via two consecutive energy transfers from Pr${}^{3+}$ to Yb${}^{3+}$ is investigated in Pr${}^{3+}$-Yb${}^{3+}$ codoped KY${}_{3}$F${}_{10}$ crystals. The efficiency of the QC second energy transfer involving the Pr${}^{3+}$ (${}^{1}$${G}_{4}$) and Yb${}^{3+}$ (${}^{2}$${F}_{5/2}$) levels is particularly difficult to determine in a precise manner since these two levels are coupled by reciprocal energy transfer. We present a specific rate equation modeling that accurately describes Pr${}^{3+}$ and Yb${}^{3+}$ dynamics and intensity ratios measured as a function of the Yb${}^{3+}$ concentration. The modeling enables to calculate energy transfer rates for all the processes and shows the competition between the two-step QC mechanism and parasitic processes. The first-step of the QC mechanism is, as expected, particularly efficient reaching 96.9$%$ and is not challenged by competing processes. The second step of the QC, while reaching an intrinsic efficiency of 75.9$%$, is plagued by backtransfers from Yb${}^{3+}$ (${}^{2}$${F}_{5/2}$) to Pr${}^{3+}$ (${}^{1}$${G}_{4}$) along with efficient concentration quenching mechanisms draining the Yb${}^{3+}$ excited-state. In addition, the investigation of intensity ratios with the Yb${}^{3+}$ concentration shows the importance of energy migration among Yb${}^{3+}$ ions that further enhances the detrimental effect of the Yb${}^{3+}$ quenching processes. As a result, the intrinsic QC efficiency (QCE) of the QC first and second energy transfers increases with the Yb${}^{3+}$ doping level up to 173$%$ in KY${}_{3}$F${}_{10}$: 0.5$%$Pr${}^{3+}$-20$%$Yb${}^{3+}$, while the real QCE reduced by migration-assisted quenching processes is only 6.2$%$ in this sample. These results clarify apparently conflicting reports found in the literature showing, on one hand, very high QCEs derived from spectroscopic experiments and, on the other hand, very low efficiency values obtained from integrating sphere measurements.

Understanding the electronic energy transfer pathways in the trimeric and hexameric aggregation state of cyanobacteria phycocyanin within the framework of Förster theory

In the present study, the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria C-phycocyanin (C-PC) were investigated in term of the Förster theory. The corresponding excited states and transition dipole moments of phycocyanobilins (PCBs) located into C-PC were examined by model chemistry in gas phase at time-dependent density functional theory (TDDFT), configuration interaction-singles (CIS), and Zerner's intermediate neglect of differential overlap (ZINDO) levels, respectively. Then, the long-range pigment-protein interactions were approximately taken into account by using polarizable continuum model (PCM) at TDDFT level to estimate the influence of protein environment on the preceding calculated physical quantities. The influence of the short-range interaction caused by aspartate residue nearby PCBs was examined as well. Only when the protonation of PCBs and its long- and short-range interactions were properly taken into account, the calculated energy transfer rates (1/K) in the framework of Förster model at TDDFT/B3LYP/6-31+G* level were in good agreement with the experimental results of C-PC monomer and trimer. Furthermore, the present calculated results suggested that the energy transfer pathway in C-PC monomer is predominant from β-155 to β-84 (1/K = 13.4 ps), however, from α-84 of one monomer to β-84 (1/K = 0.3-0.4 ps) in a neighbor monomer in C-PC trimer. In C-PC hexamer, an additional energy flow was predicted to be from β-155 (or α-84) in top trimer to adjacent β-155 (or α-84) (1/K = 0.5-2.7 ps) in bottom trimer.

Parametric Subharmonic Instability of the Internal Tide at 29°N

Abstract Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistically significant phase locking is documented between the internal tide and upward- and downward-propagating near-inertial waves. The phase between those three waves is consistent with that expected from PSI theory. Calculated energy transfer rates from the tide to near-inertial motions are modest, consistent with local dissipation rate estimates. The conclusion is that while PSI does befall the tide near a critical latitude of 29°N, it does not do so catastrophically.

Organic Solar Cells: Understanding the Role of Förster Resonance Energy Transfer

Organic solar cells have the potential to become a low-cost sustainable energy source. Understanding the photoconversion mechanism is key to the design of efficient organic solar cells. In this review, we discuss the processes involved in the photo-electron conversion mechanism, which may be subdivided into exciton harvesting, exciton transport, exciton dissociation, charge transport and extraction stages. In particular, we focus on the role of energy transfer as described by Förster resonance energy transfer (FRET) theory in the photoconversion mechanism. FRET plays a major role in exciton transport, harvesting and dissociation. The spectral absorption range of organic solar cells may be extended using sensitizers that efficiently transfer absorbed energy to the photoactive materials. The limitations of Förster theory to accurately calculate energy transfer rates are discussed. Energy transfer is the first step of an efficient two-step exciton dissociation process and may also be used to preferentially transport excitons to the heterointerface, where efficient exciton dissociation may occur. However, FRET also competes with charge transfer at the heterointerface turning it in a potential loss mechanism. An energy cascade comprising both energy transfer and charge transfer may aid in separating charges and is briefly discussed. Considering the extent to which the photo-electron conversion efficiency is governed by energy transfer, optimisation of this process offers the prospect of improved organic photovoltaic performance and thus aids in realising the potential of organic solar cells.

Computed Pore Potentials of the Nicotinic Acetylcholine Receptor

Electrostatic surface potentials in the vestibule of the nicotinic acetylcholine receptor (nAChR) were computed from structural models using the University of Houston Brownian Dynamics program to determine their effect on ion conduction and ionic selectivity. To further determine whether computed potentials accurately reflect the electrostatic environment of the channel, the potentials were used to predict the rate constants for diffusion-enhanced fluorescence energy transfer; the calculated energy transfer rates are directly comparable with those determined experimentally (see companion article by Meltzer et al. in this issue). To include any effects on the local potentials by the bound acceptor fluorophore crystal violet, its binding site was first localized within the pore by fluorescence energy transfer measurements from dansyl-C6-choline bound to the agonist sites and also by simulations of binding using Autodock. To compare the computed potentials with those determined experimentally, we used the predicted energy transfer rates from Tb 3+ chelates of varying charge to calculate an expected potential using the Boltzmann relationship. This expected potential (from −20 to −40 mV) overestimates the values determined experimentally (from −10 to −25 mV) by two- to fourfold at similar conditions of ionic strength. Although the results indicate a basic discrepancy between experimental and computed surface potentials, both methods demonstrate that the vestibular potential has a relatively small effect on conduction and selectivity.

Comparison between the calculated and measured energy transfer rates of the S3/24 state in Er3+-doped fluorozirconate glasses

The dependence of the fluorescence lifetime of the S3/24 state of the Er3+ ion on the ErF3 concentration was measured in fluorozirconate glasses at room temperature. Energy transfer rates were calculated from optical parameters assuming that the Er3+ ions in fluorozirconate glasses were dispersed as the cubic, bcc, or fcc structure, and were inserted into the rate equation. The dependence of the total transition rate of the S3/24 state of the Er3+ ion on the ErF3 concentration was calculated by using the rate equation and compared with the total transition rate measured by the lifetime experiment. Although many studies have reported the energy transfer rates in various rare-earth ions, the reliability of the calculated energy transfer rates has been hardly discussed. The energy transfer rate can be derived from the total transition rate. The energy transfer rate estimated from the rate equation calculation was compared with the energy transfer rate obtained from the lifetime measurement. It could be shown that the calculated energy transfer rate assuming that the Er3+ ions were dispersed as the cubic structure was closer to the measured energy transfer rate than that as the bcc and fcc structures. With increasing the ErF3 concentration, the calculated energy transfer rate when the Er3+ ions were dispersed as the cubic structure was comparable to the measured energy transfer rate. It was suggested that at the lower concentration of ErF3 (⩽2 mol %), we needed to use the distance between Er3+ ions which was shorter than that as the cubic structure in the calculation of the energy transfer rate.

Electron collision frequencies and energy transfer rates

The rate of energy exchange, through elastic collisions, between two gases with Maxwellian velocity distributions at different temperatures, is derived from elemetary considerations. This result is then used to calculate energy transfer rates and collision frequencies for energy transfer in plasmas at thermal disequilibrium. It is found that the electron-ion energy transfer rate and the collision frequency for energy transfer are overestimated by 5–37 per cent, depending on the electron density and the electron and ion temperatures, when the classical Coulomb logarithm ln Λ appears in these expressions. A more accurate cross section for Coulomb collisions (than that obtained when the shielded potential is truncated at the Debye length) leads to a correction term for ln Λ. Electron-electron and ion-ion collision frequencies and relaxation tunes differ from the usual expressions for these quantities by as much as a factor of two. Mean experimental and theoretical cross sections for momentum transfer for N 2, O 2, O, He and H are used to obtain simple formulas for collision frequencies and energy transfer rates useful in electron gas temperature calculations.