Reversible diffusion-influenced reactions of an isolated pair on some two dimensional surfaces.

We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the survival probability of the irreversible reaction. Furthermore, we make use of the mean reaction time approximation to write the irreversible survival probability in restricted spaces as a single exponential. In this way, we obtain exact and approximative expressions in the time domain for the reversible survival probability for three different two dimensional spatial domains: The infinite plane, the annular domain, and the surface of a sphere. Our obtained results should prove useful in the context of membrane-bound reversible diffusion-influenced reactions in cell biology.

Effects of excluded volume interaction and dimensionality on diffusion-mediated reactions.

The kinetic problem of a diffusion-mediated reaction, in which minority reactants are immobile and majority reactants are mobile, is known as the target problem. The standard theory of the target problem ignores the excluded volume interaction between the mobile reactants. Recently, a new theory of the target problem was proposed where the effect of excluded volume interaction was analytically investigated using a lattice model with prohibited double occupancy of the lattice sites. The results of that theory are approximate and need verification. In this work, we perform Monte Carlo simulations on lattices and use their results to assess the accuracy of the analytical theory. We also generalize our theory to the case of different dimensionality and perform calculations for lattices in one- and two-dimensional systems. The analytical results accurately reproduce the simulation results except in the dilute limit in one dimension. For any dimensions, the decay of the target survival probability is accelerated by the presence of excluded volume interaction.

Theory of antibunching of photon emission I.

The photon emission statistics from a single molecule containing multichromophores under pulsed excitation is theoretically studied. Fast nonradiative pair annihilation of excitons efficiently produces a single exciton, which acts as a single photon emitter. By taking into account the discrete nature of exciton numbers and the competition among pair annihilation, and unimolecular radiative and nonradiative decay of excitons, we obtain analytical expressions of photon emission statistics, the average number of emitted photons, and the normalized photon pair correlation which represents the ratio of the number of photon pairs created by the same pulse to that created by different pulses. The normalized photon pair correlation is influenced by the ratio of the pair annihilation rate to the total unimolecular decay rate including both radiative and nonradiative processes but is not influenced by the ratio of the unimolecular radiative and nonradiative rates. On the other hand, the single photon emission intensity depends on the ratio of the unimolecular radiative and nonradiative rates from the exciton left alone after pair annihilation. The conclusion is consistent with recent experimental results on conjugated polymers with various sizes in different host materials.

Accuracies of the empirical theories of the escape probability based on Eigen model and Braun model compared with the exact extension of Onsager theory.

This paper deals with the exact extension of the original Onsager theory of the escape probability to the case of finite recombination rate at nonzero reaction radius. The empirical theories based on the Eigen model and the Braun model, which are applicable in the absence and presence of an external electric field, respectively, are based on a wrong assumption that both recombination and separation processes in geminate recombination follow exponential kinetics. The accuracies of the empirical theories are examined against the exact extension of the Onsager theory. The Eigen model gives the escape probability in the absence of an electric field, which is different by a factor of 3 from the exact one. We have shown that this difference can be removed by operationally redefining the volume occupied by the dissociating partner before dissociation, which appears in the Eigen model as a parameter. The Braun model gives the escape probability in the presence of an electric field, which is significantly different from the exact one over the whole range of electric fields. Appropriate modification of the original Braun model removes the discrepancy at zero or low electric fields, but it does not affect the discrepancy at high electric fields. In all the above theories it is assumed that recombination takes place only at the reaction radius. The escape probability in the case when recombination takes place over a range of distances is also calculated and compared with that in the case of recombination only at the reaction radius.

Theory of antibunching of photon emission II.

Recently single photon emission has been observed for systems in which multiple excitons are generated by pulsed excitation. When fast pair annihilation of excitons takes place, finally a single exciton remains and single photon can be emitted. Its efficiency depends on the competition among pair annihilation, unimolecular nonradiative, and radiative processes. The efficiency of single photon emission is usually studied by measuring the correlation of emitted photons after pulsed excitation by the Hanbury-Brown and Twiss method. The photon correlation measured in this method is different from that calculated by taking into account all pairs of emitted photons, which was presented in a previous paper. We calculate the former rigorously for the first time in the case of multiple excitations and compare it with the latter. We also calculate correlation of arrival times of two photons by the Hanbury-Brown and Twiss method. These results should be useful for the analysis of the antibunching measurement by the Hanbury-Brown and Twiss method.

Distribution of the decay rate constants of individual excited probes surrounded by randomly distributed quenchers.

Recent development in single molecule spectroscopy enabled us to measure the decay kinetics of individual excited probes surrounded by randomly distributed quenchers. Since the distribution of quenchers around individual excited probes change from one excited probe to another, the quenching rate constant also changes from one excited probe to another. We calculated the distribution of quenching rate constants of individual excited probes theoretically and analyzed the observed distributions of quenching rate constants, which were recently measured by Lupton et al. [J. Phys. Chem. C 111, 11511 (2007)] by using single molecule spectroscopy.

Dynamics of barrierless and activated chemical reactions in a dispersive medium within the fractional diffusion equation approach.

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag-Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

Exact asymptotics for nonradiative migration-accelerated energy transfer in one-dimensional systems.

We study direct energy transfer by multipolar or exchange interactions between diffusive excited donor and diffusive unexcited acceptors. Extending over the case of long-range transfer of an excitation energy a nonperturbative approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally developed for contact diffusion-controlled reactions, we determine exactly long-time asymptotics of the donor decay function in one-dimensional systems.

Orientational relaxation in a dispersive dynamic medium: generalization of the Kubo-Ivanov-Anderson jump-diffusion model to include fractional environmental dynamics.

The Ivanov-Anderson model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and viscous liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first (l=1) and second (l=2) rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behavior observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.

Quantum tunneling recombination in a system of randomly distributed trapped electrons and positive ions.

During the past 10 years, quantum tunneling has been established as one of the dominant mechanisms for recombination in random distributions of electrons and positive ions, and in many dosimetric materials. Specifically quantum tunneling has been shown to be closely associated with two important effects in luminescence materials, namely long term afterglow luminescence and anomalous fading. Two of the common assumptions of quantum tunneling models based on random distributions of electrons and positive ions are: (a) An electron tunnels from a donor to the nearest acceptor, and (b) the concentration of electrons is much lower than that of positive ions at all times during the tunneling process. This paper presents theoretical studies for arbitrary relative concentrations of electrons and positive ions in the solid. Two new differential equations are derived which describe the loss of charge in the solid by tunneling, and they are solved analytically. The analytical solution compares well with the results of Monte Carlo simulations carried out in a random distribution of electrons and positive ions. Possible experimental implications of the model are discussed for tunneling phenomena in long term afterglow signals, and also for anomalous fading studies in feldspars and apatite samples.

Stochastic model of photodynamics in multichromophoric conjugated polymers.

A stochastic model of triplet exciton dynamics in multichromophoric conjugated polymers is presented and analyzed in detail, with a focus on the single molecule spectroscopy observables. The model deals with the evolution of a discrete statistical distribution of triplets in isolated polymer molecules. This approach should provide more accurate quantitative information on the dynamic processes involved, as compared to the previously used two-state model which assumes that a conjugated polymer cannot contain more than one triplet. In particular, it allows for determination of the triplet-triplet annihilation rate.

Interpretation of passive permeability measurements on lipid-bilayer vesicles. Effect of fluctuations.

A stochastic model for migration dynamics of solute molecules from the bulk aqueous phase to the intravesicular water pool is developed with a goal to interpret recent passive permeability measurements of bilayer membranes. Previously neglected fluctuations of the number of solubilized species in the inner water pool of a vesicle are naturally incorporated into the model. For a homogeneous one-phase bilayer, the model predicts exponential long-time asymptotics of the migration dynamics with a rate constant given by a sum of the frequencies of exit and entry of a solute molecule from/into the intravesicular water pool into/from the bulk aqueous phase. The long-time constant is directly related to the membrane permeability.

Lithium ion effect on electron injection from a photoexcited coumarin derivative into a TiO2 nanocrystalline film investigated by visible-to-IR ultrafast spectroscopy.

The dynamics of ultrafast electron injection from a coumarin derivative (NKX-2311), which is an efficient photosensitizer for dye-sensitized solar cells, into the conduction band of TiO(2) nanocrystalline films have been investigated by means of femtosecond transient absorption spectroscopy in a wide wavelength range from 600 nm to 10 mum. In the absence of Li(+) ions, electron injection into the TiO(2) conduction band occurred in about 300 fs. In the presence of Li(+) ions, however, electron injection occurred within approximately 100 fs, and the oxidized dye generated was found to interact with nearby Li(+) ions. Possible positions of Li(+) ion attachment to the dye molecule were examined by means of semiempirical molecular orbital calculations. The electron injection efficiency was found to increase by a factor of 1.37 in the presence of Li(+) ions. The effects of Li(+) ions on the energy of the TiO(2) conduction band and the electronic interaction between the dye molecule and Li(+) ions are discussed, and the major cause for the acceleration of electron injection was suggested to be a conduction-band shift of TiO(2).

Kinetics of diffusion-assisted reactions in microheterogeneous systems.

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.

Diffusion-mediated geminate reactions under excluded volume interactions.

In this paper, influence of crowding by inert particles on the geminate reaction kinetics is theoretically investigated. Time evolution equations for the survival probability of a geminate pair are derived from the master equation taking into account the correlation among all diffusing particles, and the results are compared with those obtained by Monte Carlo simulations. In general, excluded volume interactions by the inert particles slow down the diffusive motion of reactants. However, when the initial concentration of the inert particles is uniform and high, we show that additional influence of interference between reaction and correlated diffusion accelerates the transient decay of the survival probability in the diffusion-controlled limit. We also study the escape probability for a nonuniform initial distribution of the inert particles by taking the continuous limit in space. We show that reaction yield is increased when the reaction proceeds in the presence of a positive density gradient of the inert particles which inhibits the escape of reactants. The effect can be interpreted as a cage effect.

Reaction under vacancy-assisted diffusion at high quencher concentration.

The theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account the site blocking effects for quencher migration and the difference in the configuration of quenchers around each quencher. Our result interpolates between those in high and low limits of quencher concentrations and is a lower bound of the survival probability. In the static limit, the exact result is reproduced for a localized sink. In the presence of diffusion, the approximation is better when intrinsic reaction rates are low.

Probing the interaction of trans-resveratrol with bovine serum albumin: a fluorescence quenching study with Tachiya model.

The interaction of trans-resveratrol (TRES) and bovine serum albumin (BSA) was investigated using fluorescence spectroscopy (FS) with Tachiya model. The binding number maximum of TRES was determined to be 8.86 at 293.15 K, 23.42 at 303.15 K and 33.94 at 313.15 K and the binding mechanism analyzed in detail. The apparent binding constants (K (a)) between TRES and BSA were 5.02 x 10(4) (293.15 K), 8.89 x 10(4) (303.15 K) and 1.60 x 10(5) L mol(-1) (313.15 K), and the binding distances (r) between TRES and BSA were 2.44, 3.01, and 3.38 nm at 293.15, 303.15, and 313.15 K, respectively. The addition of TRES to BSA solution leads to the enhancement in RLS intensity, exhibiting the formation of the aggregate in solution. The negative entropy change and enthalpy change indicated that the interaction of TRES and BSA was driven mainly by van der Waals interactions and hydrogen bonds. The process of binding was a spontaneous process in which Gibbs free energy change was negative.

Unified interpretation of exciplex formation and marcus electron transfer on the basis of two-dimensional free energy surfaces.

The mechanism of exciplex formation proposed in a previous paper has been refined to show how exciplex formation and Marcus electron transfer (ET) in fluorescence quenching are related to each other. This was done by making simple calculations of the free energies of the initial (DA*) and final (D+A-) states of ET. First it was shown that the decrease in D-A distance can induce intermolecular ET even in nonpolar solvents where solvent orientational polarization is absent, and that it leads to exciplex formation. This is consistent with experimental results that exciplex is most often observed in nonpolar solvents. The calculation was then extended to ET in polar solvents where the free energies are functions of both D-A distance and solvent orientational polarization. This enabled us to discuss both exciplex formation and Marcus ET in the same D-A pair and solvent on the basis of 2-dimensional free energy surfaces. The surfaces contain more information about the rates of these reactions, the mechanism of fluorescence quenching by ET, etc., than simple reaction schemes. By changing the parameters such as the free energy change of reaction, solvent dielectric constants, etc., one can construct the free energy surfaces for various systems. The effects of free energy change of reaction and of solvent polarity on the mechanism and relative importance of exciplex formation and Marcus ET in fluorescence quenching can be well explained. The free energy surface will also be useful for discussion of other phenomena related to ET reactions.