Diffusion-controlled Bimolecular Reactions Research Articles

The Annealing Kinetics of Defects in CVD Diamond Irradiated by Xe Ions

The radiation-induced optical absorption at 1.5–5.5 eV (up to the beginning of fundamental absorption) has been analyzed in CVD diamond disks exposed to 231-MeV 132Xe ions with four fluences from 1012 to 3.8 × 1013 cm−2. The 5 mm diameter samples (thickness 0.4 mm) were prepared by Diamond Materials, Freiburg (Germany); the average grain size at growth site was around 80 μm; and the range of xenon ions was R = 11.5 μm. The intensity of several bands grows with ion fluence, thus confirming the radiation-induced origin of the defects responsible for these bands. The recovery of radiation damage has been investigated via isochronal (stepwise) thermal annealing procedure up to 650 °C, while all spectra were measured at room temperature. Based on these spectra, the annealing kinetics of several defects, in particular carbon vacancies (GR1 centers with a broad band ~2 eV) and complementary C-interstitial-related defects (~4 eV), as well as impurity-related complex defects (narrow bands around 2.5 eV) have been constructed. The experimental kinetics have also been analyzed in terms of the diffusion-controlled bimolecular reactions. The migration energies of tentatively interstitial atoms (mobile components in recombination process) are obtained, and their dependence on the irradiation fluences is discussed.

Photovoltaic Effect in Phthalocyanine-Based Organic Solar Cells: 2. Trapping of Molecular Excitons by Impurities

Trapping of molecular excitons (MEs) by ionizing impurities is a fast initial step of the photovoltaic effect in organic solar cells. Values for the ME trapping rate constant at a fixed impurity concentration NI have been found in terms of the model of diffusion-controlled bimolecular reactions. The model takes into account two pathways of quasi-steady-state ME trapping, contact and bulk capture (caused by dipole–dipole interaction with an impurity), which are determined by the ME diffusion length lS, the minimum radius of approach of partners a0, and the Forster radius RS. The trapping quantum yield at RS > a0 is YS = (1 + b)−1, where b−1 ≈ 4π(2lDRS)3/2NI. Possible doping conditions when YS ~ 1 at NI ~ 1018 cm−3 are discussed.

Distinctive features of diffusion-controlled radiation defect recombination in stoichiometric magnesium aluminate spinel single crystals and transparent polycrystalline ceramics

MgAl2O4 spinel is important optical material for harsh radiation environment and other important applications. The kinetics of thermal annealing of the basic electron (F, F+) and hole (V) centers in stoichiometric MgAl2O4 spinel irradiated by fast neutrons and protons is analyzed in terms of diffusion-controlled bimolecular reactions. Properties of MgAl2O4 single crystals and optical polycrystalline ceramics are compared. It is demonstrated that both transparent ceramics and single crystals, as well as different types of irradiation show qualitatively similar kinetics, but the effective migration energy Ea and pre-exponent D0 are strongly correlated. Such correlation is discussed in terms of the so-called Meyer-Neldel rule known in chemical kinetics of condensed matter. The results for the irradiated spinel are compared with those for sapphire, MgO and other radiation-resistant materials.

Radiation-induced defects in sapphire single crystals irradiated by a pulsed ion beam

The luminescence and thermal stability of defects formed in α-Al2O3 single crystals after powerful (300 keV) pulsed irradiation with C+/H+ ion beam were investigated. It was found by measuring of optical density, photoluminescence, and pulsed cathodoluminescence that ion irradiation induces both single F-, F+-centers and F2-type aggregate centers. An intense thermoluminescence band with a complex shape was observed in the broad temperature range of 350–700 K, its intensity decreases with increasing of the energy density of the ion beam. The thermal stability of the F-type defects produced in α-Al2O3 after irradiation with a pulsed ion beam is comparable to that in neutron-irradiated samples. The appropriate kinetics of annealing of radiation-induced defects has been analyzed in terms of the diffusion-controlled bimolecular reactions between F-type centers and complementary interstitial oxygen ions. Thus, two important kinetic parameters – the migration energy of mobile interstitials and pre-exponential – have been evaluated and discussed.

Thermal annealing of radiation damage produced by swift 132Xe ions in MgO single crystals

The annealing kinetics of the electron-type F+ and F color centers in highly pure MgO single crystals irradiated by 0.23-GeV 132Xe ions with fluences covering three orders of magnitude (Φ = 5 × 1011 –3.3 × 1014 ions/cm2) are studied experimentally via dependence of the optical absorption on preheating temperature. The annealing data are analyzed in terms of the diffusion-controlled bimolecular reactions between F-type centers and complementary interstitial oxygen ions. The behavior of the main kinetic parameters – the migration energies and pre-exponential factors – for different irradiation fluences is discussed and compared with that for other wide-gap binary materials from previous studies.

Following Bimolecular Excited-State Proton Transfer between Hydroxycoumarin and Imidazole Derivatives.

The ultrafast dynamics of a bimolecular excited-state proton transfer (ESPT) reaction between the photoacid 7-hydroxy-4-(trifluoromethyl)-1-coumarin (CouOH) and 1-methylimidazole (MI) base in aprotic chloroform- d1 solution were investigated using ultrafast transient infrared (TRIR) and transient absorption (TA) spectroscopies. The excited-state lifetime of the photoacid in solution is relatively short (52 ps), which at the millimolar photoacid and base concentrations used in our study precludes any diffusion-controlled bimolecular ESPT reactions. This allows the prompt ESPT reaction between hydrogen-bonded CouOH and MI molecules to be studied in isolation and the "contact" ESPT dynamics to be unambiguously determined. Our time-resolved studies reveal that ultrafast ESPT from the CouOH moiety to hydrogen-bonded MI molecules occurs within ∼1 ps, tracked by unequivocal spectroscopic signatures of CouO-* photoproducts that are formed in tandem with HMI+. Some of the ESPT photoproducts subsequently π-stack to form exciplexes on a ∼35 ps time scale, minimizing the attractive Coulombic forces between the oppositely charged aromatic molecules. For the concentrations of CouOH and MI used in our study (up to 8 mM), we saw no evidence for excited-state tautomerization of coumarin anions.

Recognition Kinetics of Biomolecules at the Surface of Different-Sized Spheres

Bead-based assay is widely used in many bioanalytical applications involving the attachment of proteins and other biomolecules to the surface. For further understanding of the formation of a sphere-biomolecule complex and easily optimizing the use of spheres in targeted biological applications, it is necessary to know the kinetics of the binding reaction at sphere/solution interface. In our presented work, a simple fluorescence analysis method was employed to measure the kinetics for the binding of biotin to sphere surface-bound FITC-SA, based on the fact that the fluorescence intensity of FITC was proportionally enhanced by increasing the binding amount of biotin. By monitoring the time-dependent changes of FITC fluorescence, it was found that the binding rate constant of biotin to sphere surface-immobilized FITC-SA was much smaller than that of biotin to freely diffusing FITC-SA. This can be attributed to the decreased encounter frequency of the reaction pair, restricted motion of the attached biomolecule, and the weakened steric accessibility of the binding site. These factors would become more obvious when increasing the size of the sphere upon which the FITC-SA was immobilized. Additionally, the effect of nanoparticles on the diffusion-controlled bimolecular binding reaction was more evident than that on the chemical recognition-controlled binding reaction.

Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size

We perform Monte Carlo simulations in three-dimensional (3D) lattice in order to study diffusion-controlled and mixed activation-diffusion reactions following an irreversible Michaelis–Menten scheme in crowded media. The simulation data reveal the rate coefficient dependence on time for diffusion-controlled bimolecular reactions developing in three-dimensional media with obstacles, as predicted by fractal kinetics approach. For the cases of mixed activation-diffusion reactions, the fractality of the reaction decreases as the activation control increases. We propose a modified form of the Zipf–Mandelbrot equation to describe the time dependence of the rate coefficient, k(t)=k0(1+t/τ)−h. This equation provides a good description of the fractal regime and it may be split into two terms: one that corresponds to the initial rate constant (k0) and the other one correlated with the kinetics fractality. Additionally, the proposed equation contains and links two limit expressions corresponding to short and large periods of time: k1=k0 (for t≪τ) that relates to classical kinetics and the well-known Kopelman’s equation k∼t−h (for t≫τ) associated to fractal kinetics. The τ parameter has the meaning of a crossover time between these two limiting behaviours. The value of k0 is mainly dependent on the excluded volume and the enzyme-obstacle relative size. This dependence can be explained in terms of the radius of an average confined volume that every enzyme molecule feels, and correlates very well with the crossover length obtained in previous studies of enzyme diffusion in crowding media.

Effects of the interaction potential and hydrodynamic interaction on the diffusion-influenced reaction rates

Recently, we proposed an accurate analytic expression for the diffusive propagator of a pair of particles under a central interaction potential and hydrodynamic interaction, and derived the rate expressions for fully diffusion-controlled geminate and bimolecular reactions. In this work, we present a still more accurate propagator expression, and extend the theory to the partially diffusion-controlled cases with various types of interaction potentials, including the screened Coulomb potential and the potential of mean force due to solvation. We evaluate the accuracies of our theory and other competing theories against exact numerical results. It is shown that the improved rate expressions provide near exact results for most types of interaction potentials.

Communication: Propagator for diffusive dynamics of an interacting molecular pair

We introduce a new method of solution for the Fredholm integral equations of the second kind. The method would be useful when the direct iterative approach leads to a divergent perturbation series solution. By using the method, we obtain an accurate expression of the propagator for diffusive dynamics of a pair of particles interacting via an arbitrary central potential and hydrodynamic interaction. We test the accuracy of the propagator expression by calculating the diffusion-controlled geminate and bimolecular reaction rates. It is shown that our propagator expression provides very accurate results for the whole time region.

Macroscopic description of a subdiffusion-controlled bimolecular reaction

The random trap model is used to derive equations describing reaction-subdiffusion systems with diffusion-controlled (infinitely fast) bimolecular reaction. A hierarchy of equations in terms of distribution functions is closed by using a quasi-equilibrium condition in the equation for the two-particle distribution function. The reaction terms in the resulting equations contain products between concentrations and diffusion jump rates, rather than products of concentrations as dictated by the law of mass action. The same equations are also derived in the framework of a nonlinear continuous-time random walk model. The equations are used to show that inhomogeneity of the medium may manifest itself by fractional-order reaction terms.

Femtodynamics Reflected in Nanoseconds: Bimolecular Free Electron Transfer in Nonpolar Media

The (free) electron transfer (FET) from electron donor molecules to parent solvent radical cations of alkanes and alkyl chlorides exhibits mechanistic peculiarities that are conditioned by the low polarity of these solvents. Because of the negligible solvation of ions in such systems and the almost complete lack of an activation barrier, the electron jump takes place at the very first encounter of the reactants and, as such, in extremely short times of <or=10(-15) s. Molecular oscillations (deformation, bending) occurring within the femtosecond time domain result directly in significant changes of the pi- or n-electron distribution in the HOMO ground state of the donor molecule, thereby generating a distribution of conformers. This is considered to be a rationale for a possible generation of different product radical cations in the free electron transfer, which exhibit different spin and charge distribution and, consequently different stability. Experimentally, the latter has been verified for aromatic donors, substituted with mobile, i.e., not rigidly fixed heteroatom-centered groups (various phenol type compounds, thiophenols, aromatic amines, benzyltrimethylsilanes etc.). The individually characteristic product distribution could be visualized and quantified by time-resolved spectroscopy in the nanosecond time domain. On the basis of a manifold of experimental data and supported by quantum-chemical calculations, the free electron transfer phenomenon is analyzed and discussed in detail in this summarizing report. The results presented here stand also for a, seemingly paradox, situation in which the products of a diffusion-controlled bimolecular reaction are governed by femtosecond events.

Voltammetric study of the interfacial electron transfer between bis(cyclopentadienyl)iron in 1,2-dichloroethane and in nitrobenzene and hexacyanoferrate in water

Abstract The electron transfer (ET) reaction between bis(cyclopentadienyl)iron(II) ([Fe II (C 5 H 5 ) 2 ]) in 1,2-dichloroethane (1,2-DCE) and in nitrobenzene (NB) and hexacyanoferrate redox couple ([Fe II/III (CN) 6 ] 4−/3− ) in water (W) at the interface has been studied by use of normal-pulse voltammetry. The voltammetric results indicate that the ET reaction between [Fe II (C 5 H 5 ) 2 ] in O (O = 1,2-DCE or NB) and [Fe II/III (CN) 6 ] 4−/3− in W takes place not by way of the heterogeneous ET at O|W interface but by the mechanism in which a homogeneous ET reaction between [Fe II (C 5 H 5 ) 2 ] (partially distributed from O) and [Fe III (CN) 6 ] 3− takes place in W phase and the resultant [Fe III (C 5 H 5 ) 2 ] + ion is responsible for the current passage across the interface. From the limiting current, the forward rate constants of the homogeneous ET reaction: [Fe(C 5 H 5 ) 2 ] + [Fe(CN) 6 ] 3− = [Fe(C 5 H 5 ) 2 ] + + [Fe(CN) 6 ] 4− in W phase, k f IT , were determined to be (3.2 ± 2.0) × 10 10 M −1 s −1 and (2.0 ± 1.3) × 10 10 M −1 s −1 with the 1,2-DCE|W (1.5 M Li 2 SO 4 ) and NB|W (1.5 M Li 2 SO 4 ) interfaces, respectively. These values are in the order of the rate constant of diffusion-controlled bimolecular reaction in solution. Also, the formal (standard) potentials of the transfer of [Fe(C 5 H 5 ) 2 ] + ion at the interface, Δ O W ϕ Fc + 0 , were determined to be −0.015 ± 0.014 V and −0.087 ± 0.015 V with the 1,2-DCE|W (1.5 M Li 2 SO 4 ) and NB|W (1.5 M Li 2 SO 4 ) interfaces, respectively.

Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions

Molecular-dynamics simulations are presented for the diffusion-controlled bimolecular reaction A+B<==>C in two and three dimensions. The reactants and solvent molecules are modeled as spheres interacting via continuous potential-energy functions. The interaction potential between two reactants contains a deep well that results in a reaction. When the solvent concentration is low and the reactant dynamics is essentially ballistic, the system reaches equilibrium rapidly, and the reaction follows classical kinetics with exponential decay to the equilibrium. When the solvent concentration is high the particles enter the normal diffusion regime quickly and nonclassical behavior is observed, i.e., the reactant concentrations approach equilibrium as t(-d/2) where d is the dimensionality of space. When the reaction well depth is large, however, the reaction becomes irreversible within the simulation time. In this case the reactant concentrations decay as t(-d/4). Interestingly this behavior is also observed at intermediate times for reversible reactions.

Short-Time Water Caging and Elementary Prehydration Redox Reactions in Ionic Environments

This article deals with the direct probing of water cages that assist two well-defined prehydration electron transfers (PHETs) with the reactive metal cation Cd2+. Early electron photodetachment processes are triggered by a two-photon UV excitation of aqueous halide ion Cl- (R = [H2O]/[CdCl2] = 110). Concomitant with an ultrafast Cd2+ reduction by IR p-like excited electron (J. Phys. Chem. A 1998, 102, 7795), a subpicosecond oxidoreduction reaction occurs in caged three-body complexes {Cl··e-··Cd2+}aq. Near-IR spectroscopic measurements give a PHET frequency of 1.38 ± 0.02 1012 s-1. This reduction reaction is 70 times faster than a diffusion-controlled bimolecular reaction between aqueous Cd2+ ions and fully hydrated electrons (s-state). Femtosecond spectroscopic data indicate that preexisting bridging water-molecule-bonded Cl-···Cd2+ pairs (SSIP-like configurations) assist efficient prehydration electron transfer. Because the 4s-like orbital radius of nascent {Cl··e-··Cd2+}aq configurations is larger tha...

Photophysical Deactivation Dynamics of Excited Porphyrin Molecules Adsorbed onto Dihexadecyl Phosphate Vesicles

Deactivation of triplet-excited meso-tetra(N-methyl-4-pyridyl)porphine on the surface of dihexadecyl phosphate vesicles was measured by pulsed-laser transient spectrophotometry. Both unimolecular and triplet−triplet annihilation pathways were identified from the concentration dependence of the decay profiles. The data were analyzed using the Monte Carlo method to obtain a surface diffusion coefficient for the adsorbed porphyrin of D ≈ 8 × 10-9 cm2/s at ambient temperatures. The diffusion coefficient underwent a discontinuous change at the major phase-transition temperature of the vesicles, exhibiting an Arrhenius activation energy of Ea = 31 kJ/mol below 62 °C and 7.9 kJ/mol above 62 °C. Comparisons of Monte Carlo simulations to approximate kinetic equations for diffusion-controlled bimolecular reactions confined to spherical surfaces indicate that the latter can be used to estimate diffusion coefficients for reactions on particles that are the dimensions of small unilamellar vesicles.

Kinetics and equilibrium binding of the dyes TNS and RH421 to ribulose 1,5-bisphosphate carboxylase/oxygenase (RUBISCO)

2-(p-Toluidino)naphthalene-6-sulfonate (TNS) binds in a reversible bimolecular reaction non-covalently to RUBISCO, the water-soluble enzyme for carbon dioxide fixation. TNS does not change the substrate activity at the active site of RUBISCO. Rate constants k + and k − for the association and dissociation were measured as (1.2 ± 0.2) × 10 7 dm 3 mol −1 s −1 and 1020 ± 300 s −1 , respectively. The binding of the steryl dye N-(4-sulfobutyl)-4-{4-[p-(dipentylamino)phenyl]butadienyl}pyridinium inner salt (RH421) to RUBISCO is a diffusion-controlled reversible bimolecular reaction with an association rate constant k + of (7 ± 0.6) × 10 9 dm 3 mol −1 s −1 and a dissociation rate constant k − of (1.8 ± 0.2) × 10 4 s −1 . The dissociation constants K d for the binding of TNS and RH421 to RUBISCO were calculated from the kinetically determined rate constants. These data are in good agreement with the dissociation constants measured by equilibrium techniques. Upon binding to RUBISCO the fluorescence of TNS and RH421 is more intense and blue shifted. The fluorescence lifetimes of TNS and RH421 are longer compared to those of both dyes dissolved in aqueous solution. The fluorescence anisotropy correlation time of 200 ns for TNS bound to RUBISCO corresponds to a rigidly bound dye which rotates with the same rotational correlation time as the whole protein. Both dyes can be used as probes sensitive to their molecular environment. In further experiments they were applied to the detection of ligand binding events at the active site of RUBISCO as will be described in a forthcoming publication.

Long-Range Diffusion Coefficients in Two-Dimensional Fluid Media Measured by the Pyrene Excimer Reaction

Diffusion-controlled bimolecular reactions in two-dimensional or quasi two-dimensional space are important in both surface and membrane reaction kinetics. A model reaction that has been extensively used to study the dynamics and structure of phospholipid membranes is the formation of the excimer of pyrene. We present experimental evidence that in multilamellar liposomes of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, in the fluid phase at temperatures above phase transition, TL, and for a probe/phospholipid ratio of 1:75, or lower, the fluorescence decay of 1-palmitoyl-2-(1-pyrenodecanoyl)-sn-glycero-3-phosphocholine and the time-resolved emission of the excimer follow a kinetic law specific for two-dimensional diffusion-controlled reactions. The parameters obtained from the application of this law to the experimental results, either from steady-state or from time-dependent fluorescence, give diffusion coefficients, e.g., D(25 °C) = 3.1 × 10-8 cm2 s-1 and an activation energy for diffusion, Ea = 35 k...

Nonstationary Dynamics of Excimer Formation in Two-Dimensional Fluids

A Langmuir-type film balance equipped with a fluorescence microscope for the near ultraviolet and a spectrometer for time-resolved fluorescence spectroscopic studies (suited for lifetimes ≥5 ns) was built. The aim was to study membrane dynamics of diffusion-controlled bimolecular reactions in two-dimensional fluids. Complete exclusion of molecular oxygen was achieved. Under this condition, the dynamics of excimer formation may be studied for probe concentrations as small as 0.5 mol%. At the same concentration, domain formation due to lateral phase separation may be visually observed. In the first part, the time evolution of the fluorescence of monomer and excimer in monolayers of L-α-dimyristoylphosphatidylcholine (DMPC) is studied

Diffusion-controlled bimolecular reactions: Long- and intermediate-time regimes with imperfect trapping within a Galanin approach.

We study a model for the A+B\ensuremath{\rightarrow}B diffusion-reaction system in one dimension, in which the reaction sites are modeled by a Markovian stochastic process. Mean values of the A particle density are obtained, exactly for ``dilute'' B systems and approximately for ``dense'' ones. Results are compared with numerical simulations and show good agreement in the short-, intermediate-, and long-time regimes.