Mariusz Wojcik

Fractional reaction-diffusion equation

A fractional reaction-diffusion equation is derived from a continuous time random walk model when the transport is dispersive. The exit from the encounter distance, which is described by the algebraic waiting time distribution of jump motion, interferes with the reaction at the encounter distance. Therefore, the reaction term has a memory effect. The derived equation is applied to the geminate recombination problem. The recombination is shown to depend on the intrinsic reaction rate, in contrast with the results of Sung et al. [J. Chem. Phys. 116, 2338 (2002)], which were obtained from the fractional reaction-diffusion equation where the diffusion term has a memory effect but the reaction term does not. The reactivity dependence of the recombination probability is confirmed by numerical simulations.

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.

Recombination kinetics in subdiffusive media

We study the kinetics of the recombination reaction in subdiffusive media, where the displacement of reactants r(t) follows 〈r2(t)〉∝tα with 0<α<1. We derive a rigorous fractional reaction–diffusion equation from a continuous time random walk model and calculate the kinetics of recombination reaction on the basis of this equation. The survival probability of a particle starting at r0 has an asymptotic time dependence of t−α/2 for both the perfectly absorbing and the partially reflecting boundary conditions. The change in the boundary condition alters only the coefficient for the asymptotic time dependence. The asymptotic time dependence of the survival probability is confirmed by the numerical simulations and supported by the results of a lattice model.

Geminate electron-hole recombination in organic solids in the presence of a donor-acceptor heterojunction

Geminate electron-hole recombination is one of the main factors limiting the efficiency of organic solar cells. We present a systematic study of this process based on both analytical and simulation models. We determine how the charge-pair separation probability is affected by the hopping length of charge carriers, the presence of a donor-acceptor heterojunction, electron and hole mobilities, and other factors. We show that the charge-pair separation probability of an electron and a hole which are initially at the contact distance is maximized when the electron and hole mobilities are equal to each other.

EFFECT OF AN EXTERNAL ELECTRIC FIELD ON DIFFUSION-CONTROLLED BULK ELECTRON-ION RECOMBINATION IN HIGH-MOBILITY SYSTEMS

The dependence of the rate constant of electron-ion recombination on the external electric field in systems characterized by high electron mobility is calculated by means of computer simulation. Two simulation methods are proposed, applicable for high and low electric fields, respectively. The rate constant is found to decrease with increasing electric field, the effect becomes stronger as the electron mean free time increases. Results obtained with the energy and the space criterion of recombination are discussed and a comparison of the simulation results with experimental data is included.

A study of electron recombination using highly ionizing particles in the ArgoNeuT Liquid Argon TPC

Electron recombination in highly ionizing stopping protons and deuterons is studied in the ArgoNeuT detector. The data are well modeled by either a Birks model or a modified form of the Box model. The dependence of recombination on the track angle with respect to the electric field direction is much weaker than the predictions of the Jaffe columnar theory and by theoretical-computational simulations.

Computer simulation of electron scavenging in multipair spurs in dielectric liquids

A Monte Carlo simulation was applied to model the electron scavenging processes in radiation‐induced spurs in low‐mobility liquid hydrocarbons. The scavenging probabilities were calculated for spurs containing from one to ten electron‐cation pairs, for different initial cation–cation and cation–anion distances, in a range of the scavenger concentration from 10−4 mol/dm3 to 10−1 mol/dm3. It was found that the scavenging probability decreases as the number of pairs in the spur grows. For two‐pair spurs the scavenging probability is lower by about 20%–30% as compared with the single‐pair value, for small cation–cation distances, for five‐ and ten‐pair spurs, a decrease of about 50%–60% and 60%–70%, respectively, is found. The Laplace transform technique, which converts the recombination kinetics in the absence of scavenger into the scavenging probability, is found to work reasonably well also in the multipair case. A simplified model of the fast electron track is applied to calculate the track‐averaged value...

Electron transport and electron–ion recombination in liquid argon: simulation based on the Cohen–Lekner theory

Abstract A simulation method is proposed to model the electron motion in liquid argon. The method is based on the Cohen–Lekner theory of hot electrons in liquids, and takes account of different rates of energy and momentum transfers in electron collisions. The simulation method is applied in the calculations of the electron mobility and the electron–ion recombination rate constant in liquid argon at 87 K. Agreement between the simulation results and experiment is satisfactory.

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.

Dispersive-diffusion-controlled distance-dependent recombination in amorphous semiconductors.

The photoluminescence in amorphous semiconductors decays according to the power law t(-delta) at long times. The photoluminescence is controlled by dispersive transport of electrons. The latter is usually characterized by the power alpha 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 delta=alpha/2+1 is obtained and theoretical recombination rates are compared to the kinetics of observed photoluminescence decay in the whole time range measured.