Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.     

On the temperature dependence of the rate in barrierless reactions in solution

We present a theoretical study of the temperature dependence of the relaxation rate in barrierless reactions. It is shown that a small change in the relative positions of the ground and excited potential surfaces can lead to a significant change in the relaxation rate. We suggest that a small shift of the potential surfaces, during the isoviscous temperature variation, may be responsible for the solvent-induced crossover from an apparent negative activation energy to a large positive activation energy observed in recent experiments.     

The dependence of quinine fluorescence quenching on ionic strength

The Stern-Volmer constant for the quenching of quinine fluorescence by chloride ions has been found to be markedly dependent on acid concentration. Steady-state and time-resolved fluorescence measurements under different acid and salt concentrations have further shown that the decrease in quenching arises from the influence of increasing ionic strength on the diffusion-controlled rate constant for the bimolecular quenching process. Two possible mechanisms for this dependence are discussed: a decrease in the intrinsic rate constant for the reaction due to the kinetic salt effect, and a decrease in the effective encounter distance due to screening of the charges on the reactants. © 1996 John Wiley & Sons, Inc.     

The temperature dependence and the mechanism of the SO2 (3B1) quenching reactions

The Arrhenius parameters have been determined for the SO₂(³B₁) quenching reaction (9), SO₂(³B₁) + M → (SO₂ ? M), for 21 different molecules as quenching partner M. The rate constants were calculated from phosphorescence lifetime measurements made over a range of reactant pressures and temperatures. Excitation of the SO₂ (³B₁) molecules was accomplished by two very different methods: (1) a 3829 Å laser pulse generated the triplet directly through absorption within the “forbidden” SO₂ (³B₁) → SO₂ (¹A₁) band; (2) a broadband Xe-flash system generated SO₂(³B₁) molecules and triplets were formed subsequently by intersystem crossing, SO₂(¹B₁) + M → SO₂(³B₁) + M. The measured rate constants were independent of the method of triplet formation employed. For the atmospheric gases, the activation energies (kcal/mole) were identical within the experimental error: N₂, 2.9 ± 0.4; 0₂, 3.2 ± 0.5; Ar, 2.8 ± 0.6; CO₂, 2.8 ± 0.4; CO, 2.7 ± 0.4; CH₄, 2.5 ± 0.6. This energy corresponds to the first region of the SO₂(³B₁) → SO₂(¹A₁) absorption spectra in which Brand and coworkers observe strong perturbations. It is suggested that the quenching in these cases results largely from the physical process involving potential energy surface crossing to another electronic state. Activation energies for SO₂(³B₁) quenching by the paraffinic hydrocarbons show a regular decrease in the series ethane, neopentane, propane, n-butane, cyclohexane, and isobutane, which parallels closely the decrease in C? H bond energies in these compounds. These and other data are most consistent with the dominance of chemical quenching in these cases. The rate constants for the olefinic and aromatic hydrocarbons and nitric oxide show only very small variations with temperature change, and they are near the kinetic collision number. These data support the hypothesis that quenching in these cases is associated with the formation of a charge-transfer complex and subsequent chemical interactions between the SO₂(³B₁) molecule and the π-system of these compounds.     

The anomalous temperature dependence of enzyme-catatlyzed reactions

Breaks or curvatures in the plot of log v_br vs. 1/T have been described in the literature for a number of reactions. If sufficiently small temperature intervals are used in the investigation of the temperature dependence (STI method) a trend line is obtained instead. It is then possible to distinguish regions of linear behavior and regions of anomalous behavior. The effects of e. g. the pH, the ionic strength, and added salts as well as of the size of the enzyme and substrate molecules on the anomalies were examined. The anomalous temperature dependence of the reaction rate was found to be a particularly sensitive indicator of the reaction event on the enzyme. The course of the reaction is evidently affected even by relatively small changes in conformation, particularly in the region of the active center.     

Kinetics of partly diffusion controlled reactions. I. Transient and apparent transient effect in fluorescence quenching

Analysis of decay curves of electronically excited molecules A* versus time in presence of quencher B leads to the determination of kinetic data for the reaction (i.e. for diffusion limited reactions, the experimental collisional distance σ′ greater than the true collisional distance σ) and the sum D of diffusion coefficients of both reactants). Experimental fluorescence steady state measurements (Stern-Volmer representation) are inconsistent with calculated curves using classical Smoluchowski's model with σ′and D. The difference between this has been interpreted by complex formation in the ground state between A and B. But, this assumption is unnecessary if we take into account a “static” quenching arising from B molecules located at distances between σ and σ′ from A*. A theoretical model based upon this principle is described; good agreement between the model and experimental results was obtained.     

The temperature dependence of the fluorescence lifetime of pinacyanol iodide

The fluorescence decay time of pinacyanol (1,1′-diethyl-2,2′-carbocyanine) iodide has been measured in the temperature range 95–225 K. The results indicate that two separate internal-conversion processes are operative. One of these involves torsional relaxation and is viscosity dependent.     

The dependence of the heavy atom induced quenching of the fluorescence of n-methylacridone upon the solvent

The quenching constants K and the rate constants k_q of the heavy-atom-induced fluorescence quenching of N-methylacridone were obtained from Stern-Volmer plots for nine different solvents. Iodomethane, iodoethane, iodobutane and iodobenzene were used as quenchers.It was found that the solvent dependence of K is due to the varying fluorescence decay times τ_f^w of the first excited singlet state of N-methylacridone in the solvents, whereas the values of k_q are not affected by the solvent, being appreciably smaller than the rate constants of diffusion, k_diff.The increase of k_q with decreasing ionisation potential of the quencher I_Q^V is attributed to the CT interactions between the fluorophore ¹A

and the heavy-atom quencher Q involving a CT encounter complex ¹(A

…Q), with ¹A

acting as an acceptor on account of the correlation between k_q and I_Q^V.Assuming that the formation of the encounter complex is diffusion controlled (k₁≈k_diff), the kinetics of the quenching process can be interpreted thus that the back-reaction k₋₁ proceeds at a much faster rate than the heavy-atom-induced spin inversion k_isc. The resultant small association constant k₁/k₋₁ of the CT encounter complex accounts for the weak CT interaction between N-methylacridone and heavy-atom quencher and the comparatively low values of k_q with respect to k_diff.     

Kinetics of partly diffusion controlled reactions. X. Use of a high pressure cell in fluorescence quenching experiments

The increase of the pressure over a liquid results in an increase of its viscosity, which makes possible the study of the mechanism of diffusion-controlled, or not, fluorescence quenching processes. This technique has been applied to the quenching of the fluorescence of two substituted anthraquinones by N,N-dimethyl-p-toluidine in acetonitrile solution.

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The temperature dependence of the micellisation of chlorpromazine hydrochloride in aqueous solution

The association characteristics of the weakly associating drug chlorpromazine hydrochloride have been examined over the temperature range 10–35 °C by means of conductimetric measurements. Critical micelle concentrations (cmc) have been determined by the application of a recently developed numerical method [Pérez-Rodríguez et al. (1998) Langmuir 14:4422] especially designed for the analysis of the association pattern in highly polydisperse systems of low aggregation number. The cmcs determined in this manner are used in combination with the mass-action model to obtain the thermodynamic parameters of the micellisation process, in particular the surface and hydrophobic contributions to the free energy. The use of exact forms of equations for the thermodynamics of micellisation applicable to systems of low aggregation number leads to values of the enthalpy of micellisation in reasonable agreement with experimentally determined values. Received: 6 January 2000/Accepted: 9 February 2000     

Water-induced fluorescence quenching of aniline and its derivatives in aqueous solution

Nonradiative deactivation processes of excited aniline and its derivatives in aqueous solution were investigated by steady-state and time-resolved fluorescence measurements to reveal characteristic solvent effects of water on the relaxation processes of excited organic molecules. The magnitude of nonradiative rate (k_nr) of excited aniline derivatives increased significantly in water compared to that in organic solvents (cyclohexane, ethanol, and acetonitrile). The fluorescence lifetime measurements in organic solvent/H₂O mixed solvents suggested that the fluorescence quenching in water was not due to exciplex formation but due to interactions with a water cluster. From temperature effect experiments on the fluorescence lifetime and quantum yield of aniline, N-methylaniline, and N,N-dimethylaniline, the apparent activation energies for the nonradiative deactivation rate in water were determined as 21, 30, and 41 kJ mol^-1, respectively. Upon substitution of hydrogen atoms in the aromatic ring of aniline derivatives for deuterium atoms resulted in normal deuterium isotope effect in cyclohexane, i.e. k_nr decreased by deuterium substitution, while in water the same deuterium substitution led to an increase in k_nr (the inverse isotope effect). The inverse isotope effects implied that a direct internal conversion to vibrationally higher excited states in the electronically ground state is not a dominant mechanism but the transition to a close-lying energy level, e.g. the relaxation to charge transfer to solvent (ctts) state, would be associated with the quenching mechanism in water.     

New combinatorial approach for the investigation of kinetics and temperature dependence of surface reactions in thin organic films

In this paper we present a new, simple, and reproducible method for the rapid determination of the temperature dependence of solution phase surface reactions of organic thin films on solid supports. Instead of estimating the extent of reaction for many separate samples for many different temperatures sequentially, we exploit in our new high throughput combinatorial approach surface reactions carried out under a thermal gradient followed by position-resolved contact angle (CA) measurements. The reaction kinetics, activation energies, and entropies are, thus, accessible on the basis of measurements on a very limited set of samples that differ in reaction times. The kinetics and temperature dependence of surface reactions of the previously studied alkaline hydrolysis of 11,11'-dithiobis(N-hydroxysuccinimidylundecanoate) (NHS-C10) self-assembled monolayers (SAMs) on gold, as well as the ester hydrolysis in SAMs of the novel disulfide 11,11-dithiobis(tert-butylundecanoate) (t-Bu-C10), were investigated in detail using the conventional sequential and the new combinatorial approach. The reaction kinetics, corresponding apparent rate constants k, and activation energies Ea, as well as activation entropies deltaS double dagger, determined according to both approaches agree well with each other to within the experimental error. Hence, these parameters can be quantitatively determined using the described combinatorial approach. A comparison of the reactions of the two model systems indicated that the transition state is tighter for the acid-catalyzed ester hydrolysis in SAMs of the novel disulfide t-Bu-C10 compared to the hydrolysis of the ester groups in SAMs of NHS-C10 on gold.     

Chemical kinetics of reactions in the unfrozen solution of ice

Some reactions are accelerated in ice compared to aqueous solution at higher temperatures. Accelerated reactions in ice take place mainly due to the freeze-concentration effect of solutes in an unfrozen solution at temperatures higher than the eutectic point of the solution. Pincock was the first to report an acceleration model for reactions in ice,1 which successfully simulated experimental results. We propose here a modified version of the model for reactions in ice. The new model includes the total molar change involved in reactions in ice. Furthermore, we explain why many reactions are not accelerated in ice. The acceleration of reactions can be observed in the cases of (i) second- or higher-order reactions, (ii) low concentrations, and (iii) reactions with a small activation energy. Reactions with a buffer solution or additives in order to adjust ion strength, zero- or first-order reactions, or reactions containing high reactant concentrations are not accelerated by freezing. We conclude that the acceleration of reactions in the unfrozen solution of ice is not an abnormal phenomenon.     

Influence of temperature on quenching of fluorescence in compounds of the coumarin series

A study has been made of the influence of temperature on the quantum yield of fluorescence of 3,4-benzocoumarin in ethanol or n-hexane, in the temperature interval 77–300 K. A mechanism of fluorescence quenching is proposed, consisting of thermal activation of intercombination conversion between neighboring energy levels that differ in orbital nature.Poltava Branch, Academy of Sciences of Engineering Cybernetics of the Ukraine, 3 Koval' Street, Poltava 314601, Ukraine. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 32, No. 4, pp. 247–250, July–August, 1996. Original article submitted September 26, 1995.     

Studies on the temperature dependence of methyl anthroate fluorescence

The temperature dependence of the fluorescence quantum hield φ_f of methyl-1-, methyl-2- and methyl-9-anthroate was investigated. For the former two esters, the trend of φ_f versus temperature is consistent with the mechanism proposed earlier to account for the temperature dependence of φ_f for meso-substituted anthracene. In this mechanism, an activated intersystem crossing to a nearby upper triplet is the only significant non-radiative decay mode. The activation energy E_A for fluorescence is a measure of the gap between the emitting singlet S₁ and the accepting triplet. Since the former state is more solvent dependent, solvents which lower the S₁ energy increase E_A and thereby increase φ_f. Thus E_A and φ_f are inversely related to the S₁ energy and directly related to each other. The situation for methyl-9-anthroate is quite different from that of the other esters. While E_A is inversely related to the S₁ energy, φ_f is not, and hence there is no correlation between E_A and φ_f. It appears that the φ_f of methyl-9-anthroate is more dependent on the nature of the solvent than on the measured E_A in that solvent. The inclusion of a temperature-independent non-radiative decay mode in the analysis does not produce results consistent with the above mechanism. It is suggested that the difference in behavior for these esters may in some way be related to an excited state geometry change which occurs for methyl-9-anthroate but not for the other two compounds.     

十二烷基磺酸钠增强的吡啶锉 对芘的荧光猝灭

水溶液中三种吡啶 盐(吡啶盐酸盐, HP+;N-苄基吡啶,BP^+; 苄基紫精, BV^2^+)对芘的荧光猝灭因十二烷基磺酸钠(SLS)的引入而增强, 且猝灭常数对SLS浓度的敏感性BV^2^+>BP^+>HP^+, 电导实验表明体系中无簇集体形成。认为SLS与吡啶 的静电作用及表面活性剂分子中烷基链的绕曲是导致猝灭增强的原因。     

The quenching of chlorine fluorescence in the gas phase

Laser induced fluorescence has been observed from the B³Π(O⁺_u) state of chlorine. Lifetimes have been measured from 19 to 208 Pa, but the radiative lifetime is too long to be extracted from the data. A rate coefficient of 3.2 × 10[su13] cm³ mol?1 s?1 was measured for quenching by Cl₂ or Ar, the removal process being collision induced predissociation of the ³Π(O⁺_u) state.