Size effects in triplet-triplet annihilation: I. Standard and statistical approaches

The dynamics of triplet-triplet annihilation is theoretically studied in linear chains and nanoparticles as a function of size M, the rate of excitation migration W, and the rate of excitation annihilation V. It is shown that a sum of two exponentials is usually sufficient for fitting experimental phosphorescence and triplet-triplet absorption decays. The first term describes the decay of domains containing initially one triplet, while the second term reflects the disappearance of domains containing initially two triplets.     

9，10-二杂环取代蒽衍生物制备与三线态-三线态湮灭上转换性能研究

弱光上转换是基于三线态-三线态湮灭机制将低能量(长波长)的光转换为高能量(短波长)光的一种现象,是通过光敏剂与发光剂之间能量转移实现的。针对当前上转换体系中的光敏剂研究备受关注,而对于同等重要作用的发光剂的研究甚少的现状,利用Suzuki偶联反应制备了两个新的杂环取代蒽衍生物：9,10-二(3-呋喃)蒽(DFA)和9,10-二(3-噻吩)蒽(DTA)并通过结构表征;以9,10-二杂环取代蒽为发光剂、四苯基卟啉钯衍生物(PdTPPMe和PdTPPCOOH)为三线态光敏剂,研究所构成的光敏剂/发光剂双组分体系中,三线态-三线态能量转移效率(k_Q)、发光剂的延迟荧光寿命(τ_DF)及发光剂荧光量子产率(Φ_f)等因素对上转换效率(Φ_UC)的影响。结果表明,高效三线态-三线态能量效率(Φ_TTT)、快速延迟荧光寿命和大荧光量子产率将有利于提高上转换效率。进一步研究发现,含氧发光剂(DFA)与含羧基的光敏剂(PdTPPCOOH)之间可借助氢键发生有效耦合,有利于光敏剂与发光剂之间的三线态能量转移,导致弱光上转换效率显著提高。在半导体激光器(532 nm,70 mW·cm-2)激发下获得强的绿-转-蓝上转换效率最大可达10.11%。所获得的绿-转-蓝上转换荧光可使Pt/WO₃复合半导体受激;产生氧自由基并可促使香豆素转化为7-羟基香豆素。     

Quenching of excited complexes by Fe-octaethylporphin in triplet-triplet annihilation of Mg-phthalocyanine in liquid solutions

The effect of triplet-state quenchers on the kinetics of triplet-triplet annihilation (TTA) of Mg-phthalocyanine (Mg-Phc) is studied. It is found that the rate constant of triplet-state quenching caused by TTA increases with increasing concentration [Q] of quenchers. The maximum values of the relaxation parameter of triplet states are proportional to [Q]². The experimental data correspond to TTA with the formation of TT complexes from molecules in triplet states. The proportionality of the decay rate of TT complexes into molecules in the ground state to [Q]² suggests that two quenching molecules are required for quenching one TT complex. It seems that the complex contains two locally excited triplet states of individual molecules. The spin correlation time in the triplet state seems to be longer than the average lifetime of complexes (≤10^?4 s). The quenching probability of triplet states in complexes (caused, in particular, by the energy of charge transfer) is lower than the probability of intermolecular triplet energy transfer to the quencher levels.     

Kinetics of Triplet-Triplet Annihilation in Organic Glasses

In the present paper, the results of the investigation of the decay kinetics of delayed luminescence of organic glasses are presented. A strong deviation of the decay of both phosphorescence and annihilation delayed fluorescence from the exponential law is observed. This effect is shown to be due to the relaxation process of electronic excitation energy in the system with large energetic disorder. At the same time, the presence of two time intervals in which the rate coefficient for triplet-triplet annihilation (TTA) reaction shows different dependence on time is observed. On a short time scale the classical behavior is observed, i.e., the reaction is well described by the second-order equation with a time-independent rate coefficient. At the limit of long times, we have strong dependence of rate coefficient on time, i.e., the electronic excitation energy transport is dispersive. It is shown that behavior observed for the rate coefficient for TTA reaction is due to the relaxation process (on short time scale) and the equilibrium energy migration (in long time limit).     

Determination of the rate constants of excited-complex formation and the diffusion rate constants for triplet-triplet annihilation kinetics for tetrapyrrole molecules in liquid solutions

With the flash-photolysis method, the kinetis of triplet-triplet annihilation (TTA) is investigated for a number of tetrapyrrole molecules in liquid solutions. Based on the analysis of the kinetic scheme of TTA through the formation of excited complexes (TT) a procedure for determining the constant of the rate of (TT) formation from two molecules in the triplet state (k₁) is proposed. The k₁ values obtained are equal to the rate constants for the processes controlled by molecular diffusion in the solution (K_d), which are calculated by a modified Vavilov-Debye formula. The values of K_d can be determined experimentally by the proposed procedure for processing the data on TTA. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 4, pp. 521–527, July–August, 1998.     

Intermolecular Electronic Energy Transfer in the Gas Phase

The kinetics of triplet-triplet energy transfer in the gas phase has been studied for various donor-acceptor pairs of aromatic hydrocarbons and ketones. For all the donor-acceptor pairs investigated the triplet-triplet energy transfer efficiencies are much lower than unity. The triplet triplet energy transfer was used to gain insight into the paths of intramolecular excitation energy degradation in benzophenone and anthraquinone vapours and to obtain sensitized anti-Stokes annihilation delayed fluorescence of vapours of anthracene and its derivatives.

The intermolecular triplet-triplet transfer (T-T transfer) of excitation energy and sensitized phosphorescence were first discovered in 1952 by Terenin and Yermolayev in organic solutions¹. Later these phenomena became known for liquid solutions², crystals³, and also for vapours^4-10. And though the nature of interactions underlying the T-T energy transfer phenomena in different aggregate states is the same, a number of specific features is observed in the vapour phase. The study of these processes makes it possible to obtain additional information on interacting molecules.     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

Kinetics of long-lived luminescence of eosin in Langmuir-Blodgett films

The spectral and kinetic properties of photoluminescence of mixed Langmuir-Blodgett (LB) films of eosin decyl ether and palmitic acid on a solid substrate are studied. The electronic absorption and fluorescence spectra of the films are identical to the spectra of the dye in ethanol. An increase in the dye concentration in a monolayer results in the appearance of a dimer absorption band, quenching of fluorescence of monomers, and the red shift of the spectral bands. At 90 K, the distinct phosphorescence and delayed fluorescence bands of LB films were observed. The decay kinetics of phosphorescence and delayed fluorescence is nonexponential. It is shown that the decay curve of delayed fluorescence is determined by triplet-triplet annihilation (TTA) and T ₁→S₁ triplet-singlet intersystem crossing (IS). The initial nonexponential phosphorescence decay is caused the dominant contribution of TTA to the decay of triplet molecules. The experimental data are interpreted based on the mechanisms of exchange-resonance and inductive-resonance annihilation.     

Mechanism of the electron spin polarization of excited triplet states caused by the mutual annihilation of triplet states

A new mechanism of the triplet spin polarization is considered qualitatively and quantitatively. The spin polarization arises due to the spin-selective triplet-triplet annihilation and the subsequent spin dynamics in the spin-correlated pairs of triplets. With the time-dependent perturbation theory the simple rules are found which specify the polarization pattern of triplets.     

Kinetics of Triplet-Triplet Annihilation of Mg-Phthalocyanine in Methanol and Deuteromethanol

Using the method of flash photolysis, the effect of deuteration of a solvent on the kinetics of triplet-triplet annihilation is studied on the example of Mg-phthalocyanine (Mg-Phc) in methanol-h ₄ and methanol-d ₄ at 298 K. The time and concentration kinetic dependences are different in different solvents, which cannot be explained only by the difference in the viscosity of the latter. The experimental data are analyzed based on consideration of the triplet-triplet annihilation mechanism via the formation of triplet-triplet complexes from molecules in a triplet state. It is established that in methanol-d ₄ the constants of the rates of monomolecular deactivation of the triplet state and of the decomposition of the complexes is 1.5–2 times smaller than in methanol-h ₄. The effect of deuteration is explained by the decrease in the rate of dipole-dipole energy transfer from the triplet state of the pigment to the solvent molecules in deuteration.     

A Functional-Analytic Theory¶of Vertex (Operator) Algebras, I

This paper is the first in a series of papers developing a functional-analytic theory of vertex (operator) algebras and their representations. For an arbitrary ℤ-graded finitely-generated vertex algebra (V, Y, 1) satisfying the standard grading-restriction axioms, a locally convex topological completion H of V is constructed. By the geometric interpretation of vertex (operator) algebras, there is a canonical linear map from $V⊗V to (the algebraic completion of V) realizing linearly the conformal equivalence class of a genus-zero Riemann surface with analytically parametrized boundary obtained by deleting two ordered disjoint disks from the unit disk and by giving the obvious parametrizations to the boundary components. We extend such a linear map to a linear map from $H\tilde{\otimes} H$ ( being the completed tensor product) to H, and prove the continuity of the extension. For any finitely-generated ℂ-graded V-module (W, Y _W ) satisfying the standard grading-restriction axioms, the same method also gives a topological completion H _W of W and gives the continuous extensions from to H _W of the linear maps from to realizing linearly the above conformal equivalence classes of the genus-zero Riemann surfaces with analytically parametrized boundaries. Received: 15 August 1998 / Accepted: 13 January 1999     

Single-step triplet-triplet annihilation: an intrinsic limit for the high brightness efficiency of phosphorescent organic light emitting diodes

We investigate triplet-triplet annihilation in molecular host-guest systems where triplets are localized on spatially separated guest molecules. Our results indicate that the dominant mechanism of annihilation is single-step long-range (F?rster-type) energy transfer between two excited guests. This mechanism leads to a fundamental limit for the efficiency of phosphorescent organic light emitting diodes at high luminance. Our model is confirmed by photoluminescence decay experiments on 2,3,7,8,12,13,17,18-octaethylporphine platinum as guest in a host matrix of 4,4'-N,N'-dicarbazole-biphenyl.     

Electrospinning preparation and photophysical properties of one-dimensional (1D) composite nanofibers doped with erbium(III) complexes

1D composite nanofibers of poly(vinylpyrrolidone) (PVP, M_W≈60,000) doped with three Er(III) complexes were prepared by electrospinning. They demonstrated strong near-infrared (NIR) photoluminescence (PL) at 1535 nm and ternary Er(TTA)₃Phen (denoted as Er2, where TTA=2-thenoyltrifluoroacetonate; Phen=1,10-phenanthroline) fibers (Er2/PVP) exhibited maximum PL intensity. The crystal structure of Er2 complex has been determined by X-ray diffraction measurements. Er2 doped in fibers exhibited better thermal stability of NIR PL than the pure Er2 complex. These luminescent composite fibers have potential application in optical amplifiers.     

Testing the minimal supersymmetric standard model with the mass of the <Emphasis Type="Italic">W</Emphasis> boson

We review the currently most accurate evaluation of the W boson mass, M _W , in the minimal supersymmetric standard model (MSSM). It consists of a full one-loop calculation, including the complex phase dependence, all available MSSM two-loop corrections as well as the full standard model result. We analyse the impact of the phases in the scalar quark sector on M _W and compare the prediction for M _W based on all known higher-order contributions with the experimental results.      

Electroluminescence of organic light-emitting diodes consisting of an undoped (pbi)2Ir(acac) phosphorescent layer

The electroluminescence (EL) characteristics of phosphorescent organic light-emitting diodes (OLEDs) with an undoped bis(1,2-dipheny1-1H-benzoimidazole) iridium (acetylacetonate) [(pbi)₂Ir(acac)] emissive layer (EML) of various film thicknesses were studied. The results showed that the intensity of green light emission decreased rapidly with the increasing thickness of (pbi)₂Ir(acac), which was relevant to the triplet excimer emission. It suggested that the concentration quenching of monomer emission in the undoped (pbi)₂Ir(acac) film was mainly due to the formation of triplet excimer and partly due to the triplet-triplet annihilation (TTA) and triplet-polaron annihilation (TPA). A green OLED with a maximum luminance of 26,531 cd/m², a current efficiency of 36.2 cd/A, and a power efficiency of 32.4 lm/W was obtained, when the triplet excimer emission was eliminated. Moreover, the white OLED with low efficiency roll-off was realized due to the broadened recombination zone and reduced quenching effects in the EML when no electron blocking layer was employed.     

Triplet-triplet interaction in a nearly one dimensional molecular crystal: Application to 1,4-dibromonaphtalene

The effect of a magnetic field (6 kG) on the delayed fluorescence in a 1,4-Dibromonaphtalene at 300 K and 20 K is analysed using a new approach of calculation of the triplet-triplet annihilation rate constant. The agreement of the best fit between experiment and theory allows reaching at 300 K and 20 K respectively the lifetimes and the interaction constant of the triplets pairs. Received 12 March 1999 and Received in final form 27 April 2000     

Normal and antinormal ordering of field operators in quantum optics

The relations between the probability distributionp n _vt of the number of photonsn _vt in a volumeV at timet and the probability distributions P_N(W) and P_A(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn _vt , P_N(W) and P_A(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn _vt , P_N(W) and P_A(W) become equal.     

Low-power green-to-blue and blue-to-UV upconversion in rigid polymer films

Green light excitation of platinum octaethylporphyrin (PtOEP) in poly(methyl methacrylate) (PMMA) films containing 9,10-diphenylanthracene (DPA) yielded emission of blue light under ambient conditions. This energy upconversion process was easily observed using low-power monochromatic excitation. The blue light emission arose from fluorescence of the lowest excited singlet state of DPA formed by spin-allowed annihilation of two DPA triplets excited by the transfer of the triplet energy from PtOEP to DPA. The upconversion emission intensity was proportional to the square of the excitation intensity, and an upconversion quantum efficiency of ∼0.0002 was measured at an excitation intensity of only 0.9 mW cm⁻². High concentrations of molecularly doped emitter facilitated triplet energy migration in rigid PMMA. Upconverted fluorescence was also observed from other emitters and with other sensitizers, including blue-to-UV upconversion in a PMMA film containing the non-heavy metal sensitizer 2-methoxythioxanthone and the emitter 2,5-diphenyloxazole.     

Kinetics of triplet-triplet absorption of anionic water-soluble porphyrins

It was established that in aqueous solutions of anionic porphyrins the processes of triplet-triplet (T-T) annihilation are absent (K₂<2.5·10⁵ M⁻¹ sec⁻¹), while a delayed annihilation fluorescence can be detected for these porphyrins in methanol (K₂≊3.5·10⁷ M⁻¹ sec⁻¹) and for their lipophilic analogs in organic solutions (K ₂≊2.5·10⁹ M⁻¹ sec⁻¹), and the kinetics of absorption of the latter porphyrins in triplet states is dependent on the intensity of the exciting radiation. The extremely small constant of T-T annihilation of anionic porphyrins can be due to the formation of a relatively dense solvate shell consisting of water molecules around the charged groups of the porphyrin molecules, which increases steric barriers and thus prevents an exchange-resonance transfer of energy between triplet excited molecules in aqueous solutions. It is also shown that porphyrin molecules can electrostatically repel one another when in their structure there are charged groups. To whom correspondence should be addressed. Deceased. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70 F. Skorina Ave., Minsk, 220072, Belarus; e-mail: llum@imaph.bas-net.by. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 791–795, November–December, 1999.