Monomer Excimer Kinetics Research Articles

Phasor Representation of Monomer-Excimer Kinetics: General Results and Application to Pyrene.

Phasor plots of the fluorescence intensity decay (plots of the Fourier sine transform versus the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in studies of homogeneous and heterogeneous systems. In this work, the phasor approach is applied to monomer-excimer kinetics. The results obtained allow a clear visualization of the information contained in the decays. The monomer phasor falls inside the universal circle, whereas the excimer phasor lies outside it, but within the double-exponential outer boundary curve. The monomer and excimer phasors, along with those corresponding to the two exponential components of the decays, fall on a common straight line and obey the generalized lever rule. The clockwise trajectories described by both phasors upon monomer concentration increase are identified. The phasor approach allows discussing in a single graphic not only the effect of concentration but also that of rate constants, including the evolution from irreversible kinetics to fast excited-state equilibrium upon a temperature increase. The obtained results are applied to the fluorescence decays of pyrene monomer and excimer in methylcyclohexane at room temperature. A straightforward method of monomer-excimer lifetime data analysis based on linear plots is also introduced.

How Fast is a Fast Equilibrium? A New View of Reversible Reactions

Reversible reactions are described in terms of kinetic cycles. From this description, two useful parameters arise: 1) average cycle duration and 2) average number of cycles. The latter applies to cycles with at least one unstable species. These parameters allow answering the question "How fast is a fast equilibrium?" in absolute and in relative terms, respectively. The general interest of the approach is demonstrated by application to reactions drawn from several areas: Acid-base equilibria, enzyme kinetics, excited-state proton transfer, thermally activated delayed fluorescence, monomer-excimer kinetics and homo-FRET.

Linear and convolution methods for the analysis of ground and excited state kinetics. Application to the monomer–excimer scheme

A new linear method for the determination of the rate coefficients of complex first-order (or pseudo-first-order) mechanisms is presented and applied to simulated data. The errors associated with parameter recovery are compared with those of the traditional nonlinear least-squares method. Nonlinear methods based on convolution kinetics are also developed, and general convolution equations are obtained. Special attention is paid in both cases to excited state kinetics, where concentrations are usually known only up to a constant factor. The monomer–excimer kinetics is discussed in detail, explicit relations for parameter correlation being obtained. The influence of transient effects is also quantitatively discussed.

Monomer–excimer kinetics in solution. II. Statistical nonequilibrium thermodynamic approach

The statistical nonequilibrium thermodynamic theory of diffusion-influenced reactions is employed to study reversible excimer formation in solution. Three types of rate coefficients for bimolecular excimer formation are discussed: (i) molecular rate coefficients defined by one-way reactive fluxes, (ii) phenomenological rate constants based on form of the macroscopic rate equations, and (iii) modified, time-dependent phenomenological rate coefficients. Relations are derived linking: (i) the molecular rate coefficients for reversible and irreversible excimer formation rates, and (ii) the steady-state molecular rate constant and the Laplace transform of the time resolved irreversible rate coefficient. The relationship between the present approach and the microscopic–stochastic theory of excimer formation is discussed.

Monomer–excimer kinetics in solution. I. Stochastic many-particle approach

A stochastic many-particle approach is applied to study the kinetics of reversible excimer formation in solution. Coupled dynamic equations for the macroscopic concentrations and for the radial distribution function are derived, and applied to analyze (i) time resolved kinetics after a short pulse, and (ii) steady-state kinetics. Renormalization of the phenomenological excimer dissociation rate coefficient due to nonequilibrium effects is discussed. A relation is demonstrated between steady-state, reversible monomer–excimer kinetics and irreversible fluorescence kinetics. Explicit results are given for the excimer fluorescence yield, assuming the Smoluchowski–Collins–Kimball reactivity model.

Test of a model for reversible excimer kinetics: Pyrene in cyclohexanol

A model for reversible monomer–excimer kinetics that considers the time dependence of the excimer formation rate coefficient is proposed and tested for pyrene in cyclohexanol from 25 up to 85 °C. Simultaneous analysis of the monomer and excimer experimental decay curves allows the determination of all the relevant parameters for this reaction. The diffusion coefficient follows an Arrhenius plot with activation energy of 36±1 KJ mol−1, the encounter radius varies between 7.3 and 8.9 Å, and the intrinsic rate constant for excimer formation varies between 2.4×109 and 1.1×1010 M−1 s−1. The intrinsic reciprocal lifetime of the excimer follows an Arrhenius plot with activation energy of 12±1 KJ mol−1, and the rate constant for excimer dissociation, determined for high temperatures (T>55 °C) when reversibility is important, has different values depending whether geminate pair effects are considered or not in the analysis. The binding energy of pyrene excimer obtained considering pair effects (ΔH=32±2 KJ mol−1) agrees with the published values for nonviscous solvents.

Theoretical approaches to reversible diffusion-influenced reactions: Monomer–excimer kinetics

Three formalisms that describe the influence of diffusion on the kinetics of the reversible reaction, A+B⇌AB, are discussed and compared. The simplest involves a modification of the irreversible rate equations of Smoluchowski theory; the second is based on a generalization of physically appealing convolution relations that hold rigorously for reversible reactions between isolated pairs, and the third can be obtained by using a superposition approximation to truncate the hierarchy of equations satisfied by the reactive reduced distribution functions. The various formalisms are developed to the point that their implementation requires knowledge only of the time-dependent irreversible association rate coefficient and the microscopic dissociation rate constant. All these approaches give the correct equilibrium concentrations at infinite time, have the same short-time behavior, reduce correctly when the dissociation rate is zero, and become equivalent in the reaction-controlled limit. However, none of them provides an exact treatment of the underlying many-particle diffusive model of the reaction. Some illustrative calculations are presented and the relative merits of these approaches are discussed. All three approaches predict that the relaxation of a small initial deviation of the concentrations from their equilibrium values is nonexponential, except, of course, in the reaction-controlled limit. With a view towards treating monomer–excimer kinetics, the formalisms are generalized to incorporate unimolecular decay pathways.

Diffusion-influenced excimer formation kinetics

A model for reversible monomer–excimer kinetics is developed, taking into account that different distributions of monomers around the excited ones are created by light absorption and excimer dissociation. The excimer formation rate coefficient departs from the Collins–Kimball equation owing to reversibility, originating significant deviations to Birks’ kinetics in the monomer and excimer decays. The contribution of the geminate pair created by excimer dissociation on the overall kinetics is significant for low monomer concentrations and high viscosities. Simultaneous analysis of the monomer and excimer decay curves according to the model developed should allow to extract all the relevant information concerning the excimer formation diffusion controlled process.

Time-dependent chemical reactions: A revision of monomer–excimer kinetics?

From the kinetic point of view, the fundamental quantity of a chemical reaction is the rate constant. The abundance of chemical reactions is governed by first-order kinetics. However, in many cases the diffusion of molecules in the medium leads to a diffusion-controlled chemical reaction. Among many, the monomer–excimer kinetics frequently encountered in photophysical studies is a classical example. An analysis of the kinetics of the monomer–excimer diffusionally-controlled reaction has been presented. It was shown that the theoretical results previously obtained by us using a specific technique of convolutions are in direct relation to the differential kinetic equations, provided that their solution is obtained by means of ensemble averaging. It was shown that the convolution method does not represent by itself any new method and, that it is in strict relation to more fundamental differential kinetic equations. In order to establish this relation, one cannot rely on a simple formal mathematical analysis of the differential equations, and the importance of the averaging procedure while solving the differential kinetic equations is shown. A discussion of the several aspects of differential kinetic equations is also presented.

Concentration dependence of the transient effects in monomer—excimer kinetics

Transient effects in pyrene monomer—excimer kinetics were investigated by fluorescence decay studies. The results show that, for methyl 4-(1-pyrenebutyrate), the effective capture radius R′ for the reaction in toluene in smaller than that in cyclohexane and, more surprisingly, the mutual diffusion coefficient D m in cyclohexane (but not toluene) displays a negative concentration effect.

Reversibility in monomer—excimer kinetics

A model for reversible monomer—excimer kinetics is presented, taking into account the time dependence of the excimer formation rate coefficient and making explicit distinction between the excimer formed from a monomer excited by light and the excimer formed from an excited monomer produced by the dissociation of another excimer. The respective rate coefficients of excimer formation are determined within classical diffusion theory. The results obtained, applicable to both excimer and exciplex kinetics, suggest that experimental systems should, under suitable conditions, exhibit rich kinetic behaviour not yet observed.

Transient effects in monomer–excimer kinetics

A theoretical model for diffusion-controlled excimer formation in the presence of excimer dissociation is presented. We assume that the rate coefficient for excimer formation k1(t) has the form k1(t)=a+bt−1/2. The equations obtained for monomer and excimer fluorescence decays are given in terms of Laplace transforms. Numerical analysis of monomer and excimer fluorescence decays are given in order to show the influence of dissociation, diffusion, and solution concentration on fluorescence decays. It has been shown that dissociation leads to exponentialization of decay curves. Two different methods of calculation quantum yields of monomer and excimer fluorescence are given in the case of time-dependent excimer formation and dissociation.

Excimer Fluorescence of Benzene and Its Alkyl Derivatives—Concentration and Temperature Dependence

Fluorescence spectra and quantum yields have been obtained for methylcyclohexane solutions of benzene, toluene, ethylbenzene, cumene, p-, m-, o-xylene, and 1,3,5-, 1,2,3-, 1,2,4-trimethylbenzene as a function of aromatic concentration over the temperature range from 25 to −100°C. At low temperatures distinct excimer emissions were observed for all compounds studied. The intrinsic emission quantum yields of monomer φm and of excimer φe have been determined by a simple technique which requires no assumptions regarding the details of the monomer–excimer kinetics. With decreasing temperature, φe is observed to decrease contrary to the behavior of φm, suggesting that the rate constant for the excimer radiative transition decreases strongly as the temperature is lowered. Such temperature dependence is explained as arising from the existence of a substantial vibronic component in the transition moment that is induced by thermal excitation of upper-state vibrational motions (e.g., torsional, tilting, etc.) of one monomer with respect to the other. From analysis of the temperature dependence of the fluorescence, lower bounds on the excimer binding energies Eb have been determined. The difference between this lower bound and Eb is approximately equal to the activation energy for radiative decay of the excimer. An estimate of this activation energy indicates that, for the case of benzene, Eb > 0.36 eV. The probability for association of excited monomer to form excimer and the probability for dissociation of excimer to an excited and unexcited monomer have been determined for benzene at 25 and −78°C from an appropriate analysis of the fluorescence quenching effect of CCl4. Additionally it has been demonstrated that the observed increase in CCl4 quenching efficiency at high benzene concentrations is predominantly due to an energy migration process. The probability per encounter for formation of excimer has been determined for benzene to be ≈1.0 and to decrease with alkyl substitution in a manner consistent with the steric requirements of sandwich-type excimer configurations.