282 research outputs found
Orientational relaxation in a dispersive dynamic medium : Generalization of the Kubo-Ivanov-Anderson jump diffusion model to include fractional environmental dynamics
Ivanov-Anderson (IA) 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 supercooled 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 and second 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 behaviour 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.Comment: 14 figure
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. {\bf 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.Comment: to appear in Journal of Chemical Physic
Dispersive photoluminescence decay by geminate recombination in amorphous semiconductors
The photoluminescence decay in amorphous semiconductors is described by power
law at long times. The power-law decay of photoluminescence at
long times is commonly observed but recent experiments have revealed that the
exponent, , is smaller than the value 1.5 predicted from a
geminate recombination model assuming normal diffusion. Transient currents
observed in the time-of-flight experiments are highly dispersive characterized
by the disorder parameter smaller than 1. Geminate recombination rate
should be influenced by the dispersive transport of charge carriers. In this
paper we derive the simple relation, . Not only the
exponent but also the amplitude of the decay calculated in this study is
consistent with measured photoluminescence in a-Si:H.Comment: 18pages. Submitted for the publication in Phys. Rev.
Dispersive diffusion controlled distance dependent recombination in amorphous semiconductors
The photoluminescence in amorphous semiconductors decays according to power
law at long times. The photoluminescence is controlled by
dispersive transport of electrons. The latter is usually characterized by the
power 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 is obtained and theoretical
recombination rates are compared to the kinetics of observed photoluminescence
decay in the whole time range measured.Comment: To appear in Journal of Chemical Physic
Exact asymptotics for non-radiative 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 non-perturbative
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.Comment: 16 page
Corrections to the Law of Mass Action and Properties of the Asymptotic State for Reversible Diffusion-Limited Reactions
On example of diffusion-limited reversible
reactions we re-examine two fundamental concepts of classical chemical kinetics
- the notion of "Chemical Equilibrium" and the "Law of Mass Action". We
consider a general model with distance-dependent reaction rates, such that any
pair of particles, performing standard random walks on sites of a
-dimensional lattice and being at a distance apart of each other at
time moment , may associate forming a particle at the rate .
In turn, any randomly moving particle may spontaneously dissociate at the
rate into a geminate pair of s "born" at a distance
apart of each other. Within a formally exact approach based on Gardiner's
Poisson representation method we show that the asymptotic state
attained by such diffusion-limited reactions is generally \textit{not a true
thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that
the Law of Mass Action is invalid. The classical concepts hold \text{only} in
case when the ratio does not depend on for any .Comment: 30 pages, 2 figure
Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited
The validity of two fundamental concepts of classical chemical kinetics - the
notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined
for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here
by association/dissociation reactions. We consider a
general model of long-ranged reactions, such that any pair of particles,
separated by distance , may react with probability , and
any may dissociate with probability into a geminate
pair of s separated by distance . Within an exact analytical
approach, we show that the asymptotic state attained by reversible DLR at is generally \textit{not a true thermodynamic equilibrium}, but rather
a non-equilibrium steady-state, and that the Law of Mass Action is invalid. The
classical picture holds \text{only} in physically unrealistic case when
for any value of .Comment: 4 page
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