Diffusional escaping from the well. Simple model and qualitative results

Abstract

A simple two-state model of diffusional escaping from a potential well is proposed. The two states correspond to particles inside and outside the well. Time evolution of both states is described by distribution functions (DFs). In the first state (inside the well), DF is assumed quasiequilibrium (thermal) during the escaping process. In the second state (outside the well), the evolution of DF is governed by the free diffusion equation. The escaping/capture process is approximated by a simple kinetic coupling between these two states. In the limit of high escaping and capture rates, the model reproduces almost all expressions obtained earlier for escaping kinetics by rigorous solution of the Smoluchowsky equation (SE). The model is applied to 1D escaping from the well in the presence of some other wells. The effect of interaction anisotropy on escaping kinetics is also discussed. As an example, recombination of radicals with strongly anisotropic (depending on relative orientation of radicals) interaction is considered. The kinetics is shown to be very close to exponential in this process. Magnetic field effects (MFEs) in the presence of the well are discussed briefly within the two-state model. This simple model reproduces rigorous results obtained for MFEs by the SE approach and permits some generalizations of the results.

Ultrafast dynamics for electron photodetachment from aqueous hydroxide

“…[55,56,57] This model has a number of advantages in that an explicit form for the potential is not required and it includes the diffusion dynamics. In this model, diffusion-driven escape from a potential well is treated as an equilibrium between the population in the well (d<r<a, where a is the Onsager radius at which |u(a)|=1), in which the attraction is strong, and in the potential "tail" (r>a), where this attraction is negligible.…”

“…The analysis of non-homogeneous geminate recombination kinetics in more general cases of finite reaction rates at the reaction radius and diffusion within an interaction potential can be tackled through a variety of approaches, including competitive kinetic models [53] involving different spatial sub-populations, [11] analytic and semi-analytic theories [54][55][56][57] and full numerical solution of the diffusion equation. [4,58] In each case, the initial spatial distribution of the generated pairs plays a key role.…”

External Force Affected Escape of Brownian Particles from a Potential Well

“…2,4 In the absence of force the kinetics of escaping from the spherically symmetric short range potential well u(r) is analyzed earlier. 15,16,17,18 Here we extend the approach applied in these works to describe the effect of external force. This approach is based on the approximate solution of the eq.…”

“…The well is assumed to be isotropic and highly localized (short range). Though, detailed analysis shows 16,17 that fairly deep potential well resulted, for example, from the Coulomb interaction (at large r) can also be considered as highly localized in some conditions.…”

“…In the absence of external force the kinetics of diffusion-assisted depopulation of the initially populated cage state is analyzed in detail in a number of papers. 15,16,17,18 In the limit of deep well depth the problem is shown to be accurately described with the model of two kinetically coupled states: the quasiequilibrium localized state within the well and the free diffusion state outside the well. 17 The two-state model enables one to obtain the well depopulation kinetics in a relatively simple analytical form.…”