Search

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. [ABSTRACT FROM AUTHOR]

The photoluminescence in amorphous semiconductors decays according to the power law t-δ at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power α of the transient current observed in the time-of-flight experiments. Geminate recombination occurs by radiative tunneling which has a distance dependence. In this paper, we formulate ways to calculate reaction rates and survival probabilities in the case carriers execute dispersive diffusion with long-range reactivity. The method is applied to obtain tunneling recombination rates under dispersive diffusion. The theoretical condition of observing the relation δ=α/2+1 is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured. [ABSTRACT FROM AUTHOR]

In this paper we investigate theoretically the effect of an external electric field on the rate constant of steady-state bulk diffusion-controlled reactions. We generalize previously derived results for isotropic diffusion in the absence of interparticle interaction [J. Chem. Phys. 87, 4622 (1987)] to the case where translational diffusion is anisotropic. A frequently occurring situation of transverse isotropy where Dx=Dy≠Dz is considered in detail. We derive the first-order expansion for the reaction rate constant in terms of the electric field strength E, k(E)=k(0) (1+1/2εγ), where γ=k(0)/4πRD⊥, ε=qER/kBT, q is the charge, R is the contact distance, and D⊥ is the transverse diffusion coefficient. Numerical calculations show that this first-order expansion works well in the whole range of applicability of the Nernst–Einstein relation, i.e., for ε<1. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An approximation is introduced that enables one to describe nonhomogeneous reaction–diffusion kinetics via a one-dimensional backward equation for the survival probability of a pair of particles interacting with each other through the effective potential associated with the equilibrium distance distribution in the absence of reaction. Employing the effective potential and mean reaction time approximations, the kinetics of diffusion-controlled reactions in a finite volume are analyzed, a spherical micelle being taken as a typical example of the system. A general relationship between the pseudo-first-order rate constant and the spatial arrangement of reactants is obtained. Several spatial distributions of practical importance are considered and the corresponding rate constants are calculated and compared against the existing exact analytical solutions and the results of numerical random-walk simulations. [ABSTRACT FROM AUTHOR]

Abstract: We present an analytical theory of geminate charge recombination in donor–acceptor heterojunction systems based on the Smoluchowski equation. We show that the differential equation describing this problem is mathematically equivalent to that describing geminate recombination in a four-dimensional anisotropic system. By combining this result with already available analytical results for n-dimensional homogeneous systems, we predict that the survival probability of electron–hole pairs in heterojunction systems decays as t −1 at long times. We prove this by analyzing the results of kinetic Monte Carlo simulations. We also explain clearly why the ultimate escape probability is increased by introducing the heterojunction. [Copyright &y& Elsevier]

Abstract: Non-exponential kinetics showing the induction period is observed for photoisomerization in solid phase. A possible source of the induction period is local minima along the pathway to the product which arises from the interaction of the isomerizing molecule with the surrounding molecules. In this case, multiple photoexcitations are required to complete photoisomerization. We show that product formation by photoisomerization in solid states can be analyzed by a simple equation (Eq. ). By fitting experimental data to this equation the number of local minima can be estimated. [ABSTRACT FROM AUTHOR]

Abstract: We calculate the electric field dependence of the probability of escape from geminate recombination in the case of a finite, distance-dependent intrinsic reaction rate. We solve a partial differential equation for the escape probability using a numerical method. We assess the role of finite-reactivity effects in geminate recombination and discuss their possible consequences for interpretation of experimental data. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

This article focuses on the evaluation of the reaction rates and yield of direct observation of reactive trapped holes in Titanium dioxide undergoing photocatalytic oxidation of adsorbed alcohols. The photocatalytic activity of Titanium dioxide is especially due to the oxidation power of photogenerated holes in its valence band. The hole transfer to a molecule adsorbed on the Titanium dioxide surface starts the oxidation reaction, and the oxidized molecule deviates into a final product through subsequent chemical events.