Rate Constant Of Excimer Formation Research Articles

Highly Efficient Intramolecular Excimer Formation in a Disulfide-Linked Dipyrenyl Compound: Proton Recognition and Fluidity Assessment.

Intramolecular excimer formation has been utilized extensively in chemical sciences, especially to probe solvation within complex media as well as to assess physicochemical properties of the solubilizing milieu. Pyrene has been employed extensively as a fluorescence probe for this purpose due to its favorable multidimensional fluorescence properties. Termini-capped dipyrenyl scaffolds possessing various functionalities comprise the majority of such compounds. A new both end-tagged dipyrenyl compound DTP is designed and synthesized, which exhibits significantly high intramolecular excimer formation efficiency in polar solvents. The presence of a -NH-(CO)- and/or -S-S- functionality on the chain linking the two pyrenyl groups facilitates intramolecular excimer formation. Excited-state emission intensity decay reveals that the excimer formation exclusively takes place in the excited state with only one excimer conformation. The rate constant of excimer formation is found to be higher for DTP as compared to a similar compound with an alkyl backbone. The dependence of the excimer formation on the solvent (protic versus aprotic) as well as on temperature reveals further insights into the excimer formation process. The excimer formation by DTP is found to be highly sensitive to the presence of H+: the relative excimer formation efficiency decreases drastically in the presence of a small amount of H+ (∼10-5 M). Further, the recognition of protons by DTP via intramolecular excimer formation is also observed to be highly selective in nature. Based on the observation that both the excimer formation efficiency and kinetics depend on the viscosity of the solubilizing milieu, fluidity assessment of the (dimethyl sulfoxide + acetonitrile) mixture was carried out using DTP. Further, DTP is found to be an effective probe for the assessment of the amount of water in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide as well as in a deep eutectic solvent composed of choline chloride and urea in a 1:2 mol ratio. Highly efficient and rapid intramolecular excimer formation not only establishes DTP as a useful and versatile probe but also offers strategic pathways for designing effective excimer-forming compounds.

Intramacromolecular Conformational Changes in Low Generation PAMAM Dendrimers Probed by Pyrene Excimer Formation.

Pyrene excimer formation (PEF) was used to probe the intramacromolecular conformational change experienced by low generation pyrene-labeled PAMAM dendrimers referred to as PyCX-PAMAM-GY, where X (=4, 8, or 12) and Y (=0, 1, or 2) represent the number of atoms in the pyrenyl linker and the dendrimer generation, respectively. Each sample was studied in N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) with and without 5 mM HCl. Global analysis of the monomer and excimer time-resolved fluorescence decays using the model free analysis (MFA) yielded the average rate constant of excimer formation, ⟨k⟩, which was compared with the local pyrene concentration ([Py]loc) of the PyCX-PAMAM-GY samples calculated by assuming that the oligomeric segments constituting the dendrimer's interior obeyed Gaussian statistics. A notable decrease in ⟨k⟩ was observed upon the addition of 5 mM HCl to the PyCX-PAMAM-GY solutions and was attributed to swelling of the dendrimers resulting from the protonation of the internal tertiary amines. The reversibility of this conformational change could also be monitored via PEF. Solvent differences between DMF and DMSO were accounted for by dividing ⟨k⟩ by kdiff, the bimolecular rate constant for diffusive PEF of a n-hexyl-1-pyrenebutyramide model compound, to yield the ⟨k⟩/kdiff ratio. Comparison between the ⟨k⟩/kdiff ratios obtained for all the PyCX-PAMAM-GY samples with and without 5 mM HCl revealed a 13% increase in the radius of the PAMAM-GY dendrimers upon protonation of their internal tertiary amines in agreement with earlier reports. These experiments illustrate that PEF represents a powerful experimental means to quantitatively probe the intramacromolecular conformational changes of complex macromolecules in solution, in a manner that complements scattering techniques.

Characterization of the Distribution of Pyrene Molecules in Confined Geometries with the Model Free Analysis.

Evidence is provided showing that global Model Free Analysis (MFA) of monomer and excimer fluorescence decays of pyrene dissolved in aqueous solutions of sodium dodecyl sulfate (SDS) provides the same structural and dynamic information on SDS micelles as the well-established Micelle Model (MM) does. Both MFA and MM were employed to characterize the quenching kinetics between dyes and quenchers located in surfactant micelles and the aggregation number of surfactant micelles. However, contrary to the MM, which assumes that dyes and quenchers distribute themselves among SDS micelles according to a Poisson distribution and react with a rate constant that is proportional to the number of reactants in a micelle, the MFA accomplishes this task without making any assumption about the process of pyrene excimer formation in SDS micelles. The ability of the MFA to retrieve accurately the molar fraction of pyrene molecules that are isolated in SDS micelles and do not form excimers was taken advantage of to establish that it equaled the Poisson probability of exciting micelles that contained a single pyrene. The molar fraction of isolated pyrenes could then be utilized to determine the aggregation number of the SDS micelles, and the rate constant of excimer formation between one excited- and one ground-state pyrene located inside a same micelle. Within experimental error, both the MFA and MM yielded the same micelle aggregation number and rate constant of excimer formation, with the MFA making no prior assumptions about the physical principles underlying the process of excimer formation contrary to the MM. The ability of the MFA to retrieve quantitative parameters providing structural and dynamic information about macromolecular systems with no prior knowledge about their architecture or labeling scheme implies that it can be applied to characterize a wide range of macromolecular architectures in solution.

Probing Side Chain Dynamics of Branched Macromolecules by Pyrene Excimer Fluorescence

Four different pyrene-labeled polymers were prepared by radical copolymerization of n-butyl methacrylate (BMA) and 1-pyrenemethyl methacrylate (PyEG0-MA), 1-pyrenemethoxyethyl methacrylate (PyEG1-MA), 1-pyrenemethoxyethoxyethyl methacrylate (PyEG2-MA), and 1-pyrenemethoxydiethoxyethyl methacrylate (PyEG3-MA) to yield PyEG0–PBMA, PyEG1–PBMA, PyEG2–PBMA, and PyEG3–PBMA, respectively. The only structural difference between the polymers was the length of the oligo(ethylene glycol) spacer separating the pyrene label from the main chain. Steady-state and time-resolved fluorescence were applied to investigate how the length of the spacer affected the photophysical properties of the pyrene-labeled polymers. Excimer formation between an excited-state and a ground-state pyrene was enhanced by a longer spacer which increased the probability of encounter between two pyrene labels. This conclusion was supported through the analysis of the fluorescence decays of the polymers according to the fluorescence blob model (FBM) which yielded the number (Nblob) of monomers constituting the volume in the polymer coil probed by an excited pyrene and the rate constant of excimer formation, kblob, inside a blob. Nblob increased more or less linearly with increasing spacer length reflecting a larger blob volume. kblob for PyEG0–PBMA was small due to steric hindrance while kblob took a larger but similar value within experimental error for all polymers labeled with pyrene derivatives having oligo(ethylene glycol) spacers. These experiments demonstrate that for a branched macromolecule the volume probed by the tip of a side chain and its dynamics can be characterized quantitatively by monitoring pyrene excimer fluorescence. They are expected to provide important dynamic and structural information about the numerous highly branched macromolecules that are currently under intense scientific scrutiny.

Synthesis and photophysical studies of new pyrenylamino acids

Two new pyrenylamino acid derivatives were synthesized from β-bromodehydroalanine derivatives in good yields using addition and elimination reactions.The photophysical properties of the two new pyrenylamino acids were studied in several solvents. Steady-state and time-resolved fluorescence measurements revealed that the bipyrenylamino acid undergoes excimer formation, this process being solvent dependent. Rate constants for excimer formation and dissociation were calculated. The monopyrenylamino acid exhibits a photophysical behavior similar to that of pyrene, including the sensitivity to solvent polarity.The results point to a potential use of these new pyrenyl derivatives as fluorescent probes for peptides and proteins.

A Study of the Dynamics of the Branch Ends of a Series of Pyrene-Labeled Dendrimers Based on Pyrene Excimer Formation

A series of pyrene-labeled dendrimers were prepared from generation n = 1 to n = 4 where the pyrenes were attached to the end groups of the dendrimers. Pyrene excimer formation was monitored by steady-state and time-resolved fluorescence spectroscopy as a function of generation number and in terms of the I(E)/I(M) ratio and the average rate constant of excimer formation <k>. To account for the unconventional distribution of pyrene labels which were neither randomly distributed throughout the macromolecule nor limited to just two units which are the only two pyrene-labeling schemes that can be dealt with in a straightforward manner, a Model Free (MF) analysis was applied to the global analysis of the fluorescence decays. Within experimental error, the I(E)/I(M) ratios and <k> obtained from, respectively, the steady-state fluorescence spectra and the time-resolved fluorescence decays were found to increase linearly with increasing generation number. This result is inconsistent with the fact that both the I(E)/I(M) ratio and <k> are proportional to the local concentration of pyrene inside the dendrimer ([Py](loc)) which is not expected to increase with generation number if the excited pyrene is assumed to diffuse freely throughout the dendrimer interior. Since the core-dense model predicts that the dendrimer terminal ends can occupy any position throughout the dendrimer interior, these results suggest that excimer formation between the pyrene-labeled ends is enhanced due to the branched nature of the dendrimer.

Fluorescence Behavior of a Pyrene-End-Capped Poly(ethylene oxide) in Organic Solvents and in Dioxane−Water Mixtures

A poly(ethylene oxide) polymer end-labeled with two pyrene units (M(w) = 9500 g/mol and abbreviated as Py(2)PEO) was investigated in dioxane-water mixtures and several organic solvents by steady-state and time-resolved fluorescence techniques. In dioxane-water mixtures, the fluorescence emission spectra indicate that with the gradual addition of dioxane to the solvent mixture, the maximum of the pyrene monomer band remains practically constant, whereas the excimer band displays a blue shift of approximately 8-10 nm. From time-resolved fluorescence data, two- and three-exponential decays at the pyrene monomer and excimer emission wavelengths, respectively, were obtained. Two of the decay times (tau(1) and tau(2)) are identical at all emission wavelengths. The additional shorter decay time (tau(3)), which is only observed at the excimer emission wavelength, was attributed to the component responsible for the blue-shifted excimer maximum, that is, to a second excimer, uncoupled to the other two species. Thus, the time-resolved fluorescence data suggests that one pyrene monomer is able to form either one or two excimers (E(1) and E(2), coupled and uncoupled, respectively). The sum of the pre-exponential factors, associated with the coupled species, at the excimer emission wavelength in dioxane-water mixtures always differs from zero. This, together with differences in the excitation spectra when collected at the monomer and excimer wavelengths, revealed that a static route is partially responsible for E(1)* formation. In the case of pure organic solvents, the proposed kinetic scheme can be simplified. In this case, the sum of the pre-exponential factors at the excimer emission wavelength is practically zero, which is a direct consequence of the dynamic mechanism being the only route for E(1)* formation. The kinetic scheme has been solved, and the rate constants for excimer formation (k(a)), dissociation (k(d)), and excimer decay (k(E)) are presented.

Energetics and Dynamics of Naphthalene Polyaminic Derivatives. Influence of Structural Design in the Balance Static vs Dynamic Excimer Formation

Two new fluorescent macrocyclic structures bearing two naphthalene (Np) units at both ends of a cyclic polyaminic chain were investigated with potentiometric, fluorescence (steady-state and time-resolved) and laser flash photolysis techniques. The fluorescence emission studies show the presence of an excimer species whose formation depends on the protonation state of the polyamine chains implying the existence of a bending movement (occurring in both the ground and in the first singlet excited state), which allows the two naphthalene units to approach and interact. For comparison purposes, one bis-chromophoric compound containing a rigid chain (piperazine unit) was also investigated. Its emission spectra shows a unique band decaying single exponentially thus showing that no excimer is formed. With the two new ligands, excimer formation occurs in all situations even at very acidic pH values when the protonation of the polyamine bridges is extensive. Coexistence of ground-state dimers with dynamic excimers was established based on steady-state and timeresolved fluorescence data. The energetics of excimer formation and dissociation were determined in ethanol and water. Different methods of decay analysis (independent decay deconvolution, global analysis and excimer deconvolution with monomer) were used to extract the kinetic (rate constants for excimer formation, dissociation, and decay) and thermodynamic parameters. In ethanol and acidified ethanol:water mixtures, an additional short decay time was found to exist and assigned to a dimer, whose presence is assumed to be responsible by the decrease in activation energy for excimer formation in this solvent. The results are globally discussed in terms of the small architectural differences that can induce significant changes in the photophysical behavior of the three studied compounds.

Time-Resolved and Steady-State Fluorescence Studies of Hydrophobically Modified Water-Soluble Polymers

A comprehensive study of the photophysical behavior of poly(acrylic acids) randomly labeled with pyrene using steady-state and time-resolved fluorescence spectroscopy is presented. The influence of external factors, such as different solvents and pH in the aqueous solution, on the polymer photophysics has been investigated. These factors induce major changes in the polymer conformation, which are reflected in the fluorescence experiments. The random introduction of the hydrophobic pyrene groups along the macromolecule favors the coexistence of static (preformed dimers) and dynamic (excimers) monomer quenching phenomena together with a fraction of isolated monomers (not able to form excimer), as revealed by time-resolved and steady-state fluorescence data. In dioxane and methanol solvents, the global analysis of the fluorescence time profiles shows a rise time of similar to21-32 ns followed by a decay of similar to90-138 ns with an additional long r decay component with a low preexponential factor. This is consistent with the fact that in organic solvents such as methanol and dioxane, which are considered to be good solvents, the fraction of preassociated and isolated chromophores is highly reduced and excimer formation is essentially due to a dynamic mechanism. A kinetic scheme involving two types of monomers (M-A and M-B) and one excimer (E) is proposed. From the fluorescence decays it was possible to extract quantitatively the percentage of ground-state preformed dimers along with the percentage of isolated chromophores at room temperature. In addition, it is shown that the fraction of associated ground-state chromophores that can be excited is always larger than that of the isolated chromophores. The rate constants for excimer formation (k(a)), dissociation (k(d)), and deactivation (k(E)) were determined considering the absence and presence of preformed dimers. Additional photophysical and spectroscopic data consisting of wavelength shifts, peak- o-valley ratios and differences (obtained both from absorption and from excitation spectra collected at the monomer and excimer emission region), and the vibronic I-1/I-3 ratio in the pyrene monomer emission were found to be pH-dependent for the polymers in aqueous solution. Hence, by combining the results from steady-state fluorescence measurements with time-resolved fluorescence data, information is provided on how the chain conformation of the labeled PAA polymers changes depending on the solvent (water at different pH values or organic solvents). In water, the conformation changes from compact at low pH to an open polymer coil at high pH, whereas the polymers are in an extended state when in dioxane and methanol. (Less)

Dynamics of Cyclic Methylphenyltrisiloxane in the Picosecond to Nanosecond Time Range

The dynamics of the cyclic trimer of methylphenyl-substituted siloxane (1,3,5-triphenyl-1,3,5-trimethylcyclotrisiloxane; CMPS3) in dilute methylcyclohexane solution was probed with picosecond time-resolved and steady-state fluorescence in a wide range of temperatures (20 to −100 °C) from the high-temperature limit to the low-temperature limit. The crossover between these two regimes is found around −30 °C. Monomer and excimer decays are triexponential, with one of the three components coming from the monomer that is unable to form excimer with its neighboring chromophores (the lone phenyl ring in the trans isomer of CMPS3). A kinetic mechanism is developed that takes into account preformed dimers, lone monomers, and also energy transfer from these lone monomers to excimer-forming ones. With such a mechanism, the rate constants for excimer formation (ka) and excimer dissociation (kd), as well as the corresponding activation energies (Ea, Ed), are obtained from the decays. The rate constants are high (ka = 13.7 × 109 s-1 at 20 °C) and the activation energies are low (Ea = 2.2 kcal mol-1) compared with C−C molecules; however, their values for this small cycle are very similar to those for long linear chains of poly(methylphenylsiloxane). Thus, although the cycle is somewhat strained and has a greater fraction of isolated monomers and a smaller fraction of preformed dimers than the linear polymer, the main factor that determines excimer kinetics in both types of structures is their common conformational flexibility of the siloxane backbone. The kinetic mechanism developed succeeds in giving a fraction of photophysically hindered monomers (∼0.23) in total agreement with the fraction of trans phenyl rings (0.23 determined from 1H NMR) and also in giving a rate constant for excited monomer energy transfer independent of temperature.

Excimer formation of cyanobiphenyls in calix[4]resorecinarene derivative probed by picosecond time-resolved fluorescence spectroscopy

Excimer formation kinetics of cyanobiphenyls (CB), which are linked in a parallel direction to a calix[4]resorecinarene (CRA), has been examined by means of a picosecond time-resolved fluorescence spectroscopy. From fluorescence decay analyses, the rate constant of excimer formation is estimated to be k 3 = 1.9 × 10 9 s −1 and that of dissociation to be k 4 = 4 × 10 7 s −1. These values are significantly smaller than those for a liquid crystal of 4-cyano-4′-octyloxybiphenyl (8OCB). The parallel orientation of CB groups in CRA may hinder the excimer formation, in contrast to those in the 8OCB liquid crystal in which the CB's form a weakly coupled antiparallel dimer in the ground state.

The kinetic parameters for intramolecular excimer formation from the meso and racemic diastereoisomers of 2,4-DI(2-pyrenyl) pentane: evidence for rapid conformer interconversion

Absorption and fluorescence spectra of the meso and racemic diastereoisomers of 2,4-di(2-pyrenyl)pentane (2DPP) which form intramolecular excimers in methylcyclohexane at 25° C are presented. From time-correlated single-photon counting measurements of the double-exponential monomer and excimer fluorescence decays, the rate constants for excimer formation and dissociation and the excimer lifetime have been determined. These data are compared with similar data obtained for the related compounds 1,3-di(2-pyrenyl) propane and l,3-di(2-pyrenyl) butane. It is concluded that the singlet excited state monomer conformers of 2DPP interconvert on a subnanosecond time scale.

Fluorescence decay of pyrene in small and large unilamellar L, alpha-dipalmitoylphosphatidylcholine vesicles above and below the phase transition temperature.

The fluorescence decays of pyrene in small and large unilamellar L, alpha-dipalmitoylphosphatidylcholine vesicles have been investigated as a function of probe concentration and temperature. When the molar ratio of pyrene to phospholipid equals 1:3000, no excimer emission is observed and the fluorescence decays are mono-exponential. When this ratio is equal to or higher than 1:120, excimer formation is observed. Above the phase transition temperature the observed fluorescence decays of monomer and excimer can be adequately described by a bi-exponential function. The monomer decays can be equally well fitted to a decay law which takes into account a time-dependence in the probe diffusion rate constant. The fluorescence decay kinetics are compatible with the excimer formation scheme which is valid in an isotropic medium. The excimer lifetime and the (apparent) rate constant of excimer formation have been determined as a function of probe concentration at different temperatures above the phase transition temperature. The activation energy of excimer formation is found to be 29.4 +/- 1.3 kJ/mol. In small unilamellar vesicles the diffusion constant associated with the pyrene excimer formation process varies from 8.0 X 10(-7) cm2/s at 40 degrees C to 2.2 X 10(-6) cm2/s at 70 degrees C. Below the phase transition temperature the monomer decays can be described by a decay law which takes into account a time dependence of the rate constant of excimer formation. The lateral diffusion coefficient of pyrene calculated from the decay fitting parameters of the monomer region varies from 4.0 X 10(-9) cm2/s at 20 degrees C to 7.9 X 10(-8) cm2/s at 35 degrees C. No significant difference could be observed between the pyrene fluorescence decay kinetics in small and large unilamellar vesicles.

Intramolecular excimer formation of oligostyrenes from dimer to tridecamer: The measurements of rate constants for excimer formation, singlet energy migration, and relaxation of internal rotation

The emission properties of styrene oligomers from dimer to tridecamer have been investigated by picosecond pulse radiolysis at room temperature. The oligomers are precisely fractionated and are considered to be models of atactic polystyrene. The rate constant for excimer formation kDM of the order of 108 s−1, increases with increasing number of monomer units n for 2≤n≤8, then levels off at the value for polystyrene. The rate constant for singlet energy migration between adjacent chromophores in polystyrene was determined to be 3×1010 s−1 (∼30 ps). An average time of 7.2 ns was found to be necessary for two adjacent chromophores to assume the excimer conformation (g−t or tg− in a racemo dyad; tt in a meso dyad) from their initial equilibrium distribution of conformations. The present result is an indication that one may investigate the dynamics of internal rotation by photophysical techniques. Moreover, from a comparison of the results of photostationary measurements with those of transient methods, it is found that there is a discrepancy between them. This discrepancy is assumed to be caused by a molecular weight dependence either of the rate constant for the radiative deactivation from the excited monomer singlet kFM or of intramolecular self-quenching.

Intramolecular excimer formation in aqueous solutions of sodium poly(styrenesulfonate)

Monomer and excimer emissions are observed in aqueous solutions of sodium poly(styrenesu1fonate). The excimer-to-monomer emission intensity ratios (ZEIZM) are between 1 and 2.1 and increase with polymer concentration. From measurements of ZE/IM and the lifetimes of these emissions, the rate constants for excimer formation, dissociation, and radiative and nonradiative deactivation processes, and the quenching constants with CoS04 and NaN02, are estimated. The contributions of the regular configurational alignment of the hydrophilic and hydrophobic moieties of the polymer and the electrostatic interactions between monomer units are suggested to be the main factors controlling excimer formation.

Formation of KrCl * and ArCl * molecules and radiative lifetimes of their B states investigated with selective synchrotron radiation excitation

Monochromatic pulsed VUV excitation of Cl 2 or inert gas atoms in Cl 2 doped Kr and Ar leads to formation of KrCl * and ArCl *. The radiative lifetimes of the B states (KrCl * 19 ns, ArCl * 9 ns) and rate constants for excimer formation, quenching and collisional mixing of B and C states are given. The radiative lifetime and the quenching rate increase with vibrational excitation of the B state (KrCl *).

Steric effects on excimer formation in isotactic and atactic polystyrene and poly(ar‐methylstyrene)s in solution

AbstractEffects of tacticity and steric hindrance on excimer formation were investigated in isotactic and atactic polystyrene, poly(o‐methylstyrene), poly(m‐methylstyrene), and poly(p‐methylstyrene) in the presence and absence of a quencher (CCl4). The calculated rate constants for excimer formation in the isotactic polymers except for poly(o‐methylstyrene) were almost the same and larger than those in the corresponding atactic polymers. These results indicate that excimer formation was due to not only rotational sampling but also energy migration to trapping sites. It was found that steric hindrance on excimer formation was intimately related to the excition diffusion length in the polymer chain.

Lateral diffusion in the hydrophobic region of membranes: use of pyrene excimers as optical probes

A new (optical) method of diffusion measurement is described which allows the determination of the coefficient of lateral diffusion, D diff, of aromatic molecules in the hydrophobic region of lipid bilayers. In the present work pyrene is used as a fluorescence probe. The method is based on the finding that the formation of excited pyrene dimers (excimers) in fluid membranes is a diffusion controlled process. The value of D diff is obtained from the second order rate constant of excimer formation which is determined from the ratio of the excimer to the monomer fluorescence quantum yields The method has been applied to dipalmitoyllecithin membranes and mixed dipalmitoyllecithin-cholesterol bilayers. The diffusion coefficient for pyrene in dipalmitoyllecithin membranes at 50 °C (that is above the lipid phase transition) is D diff = 1.4 · 10 −7 cm 2/s. The activation energy for the pyrene diffusion is ΔE = 8.8 kcal/mole. Below the lipid phase transition pyrene aggregates into small clusters embedded in the lipid matrix. For bilayers of unsonicated lipid dispersions the cluster formation is observed at very low pyrene concentration of 0.1 mole %, showing that the lipid matrix forms a rather regular crystal structure. Above the lipid phase transition cholesterol reduces the lateral mobility of pyrene considerably (at 30 mole cholesterol: D diff = 0.64 · 10 −7 cm 2/s). Below the phase transition cholesterol suppresses the cluster formation. The excimer formation of pyrene is also sensitive to the pretransition of the lipid matrix occurring about 10 °C below the main lipid phase transition at T t = 41 °C.

Intramolekulare Excimere: Die Kinetik ihrer Bildung und Desaktivierung

A set of kinetic equations has been developed which allows to calculate the rate parameters of intramolecular excimer formation, dissociation and of radiative and non-radiative desactivation processes. Experimental data necessary for evaluating the equations are monomer lifetime and relative fluorescence intensities of monomer and excimer fluorescence in solution with and without added quenching substance. Spectroscopical data of biscarbazolyl propane, diphenyl propane and derivatives are used in order to calculate the rate constants. It is shown that the stronger excimer fluorescence of diphenyl propane, as compared with biscarbazolyl propane, is due to the high rate constant of excimer formation in the former substance