Anomalous growth of the depletion zone in the photobleaching trapping reaction

Absence of depletion zone effects for the trapping reaction in complex networks

In the present work we examine in detail the formation of a depletion zone in the trapping reaction in networks, with a single perfect trap. We monitor the particle density rho(r) with respect to the distance r from the trap. We show using Monte Carlo simulations that the depletion zone is absent in regular, Erdos-Renyi (ER), and scale-free (SF) networks. The density profiles show significant differences for these cases. The particles are homogeneously distributed in regular and ER networks with the depletion effect appearing in very sparse ER networks. In SF networks we reveal the important role of the hubs, which due to their high random walk centrality are critical in the trapping reaction. In addition, the degree distribution plays a significant role in the distribution of the particles recovering the depletion zone formation for high gamma values. The mean connectivity of the network is found to play a significant role in both ER and SF networks.

Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation

The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic nonzero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t(-1/4) and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found.

Scaling Theory in a Model of Corrosion and Passivation

We study a model for corrosion and passivation of a metallic surface after small damage of its protective layer using scaling arguments and simulation. We focus on the transition between an initial regime of slow corrosion rate (pit nucleation) to a regime of rapid corrosion (propagation of the pit), which takes place at the so-called incubation time. The model is defined in a lattice in which the states of the sites represent the possible states of the metal (bulk, reactive, and passive) and the solution (neutral, acidic, or basic). Simple probabilistic rules describe passivation of the metal surface, dissolution of the passive layer, which is enhanced in acidic media, and spatially separated electrochemical reactions, which may create pH inhomogeneities in the solution. On the basis of a suitable matching of characteristic times of creation and annihilation of pH inhomogeneities in the solution, our scaling theory estimates the average radius of the dissolved region at the incubation time as a function of the model parameters. Among the main consequences, that radius decreases with the rate of spatially separated reactions and the rate of dissolution in acidic media, and it increases with the diffusion coefficient of H(+) and OH(-) ions in solution. The average incubation time can be written as the sum of a series of characteristic times for the slow dissolution in neutral media, until significant pH inhomogeneities are observed in the dissolved cavity. Despite having a more complex dependence on the model parameters, it is shown that the average incubation time linearly increases with the rate of dissolution in neutral media, under the reasonable assumption that this is the slowest rate of the process. Our theoretical predictions are expected to apply in realistic ranges of values of the model parameters. They are confirmed by numerical simulation in two-dimensional lattices, and the expected extension of the theory to three dimensions is discussed.

Effect of a slit-shaped trap on depletion kinetics within a microchannel

The diffusion-limited trapping reaction kinetics of the growth of the depletion zone within and around a "slit-shaped" trap in a flat microchannel was studied experimentally and numerically. In the experiment, an ellipse-shaped laser beam acted as a slit trap in a long, flat capillary, and the trapping reaction is photobleaching of fluorescein dye. The parameter studied was the theta distance, i.e., the distance from the trap to the point where the reactant concentration has been locally depleted to the specific survival fraction [theta] of its initial bulk value. When the trap is perfect, then, due to the geometry of the trap and the reactor, as many as three time regimes can be found, with up to two crossover transitions. The number of crossovers is determined by the relative sizes of the trap and the microreactor. In the case of two crossovers, we show that the first crossover relates to the length of the trap, while the second crossover relates to the width of the reactor. When the slit trap is imperfect and its width cannot be neglected, as is the case in the experiments, a nontrivial early behavior is observed, followed by two regions in time, separated by a single crossover only.

Depletion kinetics in the photobleaching trapping reaction inside a flat microchannel

The diffusion-limited kinetics of the growth of a depletion zone around a static point trap in a thin, long channel geometry was studied using a laser photobleaching experiment of fluorescein dye inside a flat rectangular capillary. The dynamics of the depletion zone was monitored by the theta distance, defined as the distance from the trap to the point where the reactant concentration has been locally depleted to the specified survival fraction (theta) of its initial bulk value. A dimensional crossover from two dimensions to one dimension, due to the finite width of the reaction zone, was observed. We define a "parallel" and a "perpendicular" theta distance, along the slab long and short dimensions, respectively, and study their time development as a means to study the asymmetrical nature of the slab geometry. For all theta values, the crossover occurs concurrently for both theta distances when the depletion zone touches the boundary for the first time. We derive theoretical expressions for this geometry and compare them with the experimental data. We also obtain important insight from the ratio of the reactant concentration profiles in the parallel and perpendicular directions. Exact enumeration and Monte Carlo simulations support the anomalous depletion scaling results. Nevertheless, the crossover time (tau(c)) is still found to scale with the width (W) of the rectangular reaction zone as tau(c) approximately W2 , as expected from the basic Einstein diffusion law.

Dynamics of the depletion zone at a finite-sized imperfect trap in two dimensions: photobleaching experiments and simulations

The kinetics of the growth of depletion zones around a static trap in an effective two-dimensional geometry were studied experimentally with photobleaching of fluorescein dye by a focused laser beam. The phototrap served as an imperfect trap with a finite size. The growth of the depletion zone was monitored by the theta distance, defined as the distance from the trap to the point where the concentration of the reactants reaches a given arbitrary fraction theta (0<theta<1) of its initial value, which could be directly measured experimentally. At the asymptotic limit, the results confirm the theoretical nonuniversal t(theta/2) scaling behavior for the theta distance. We also find an effect of fast expansion at an early time of the depletion zone inside an imperfect trap. Both the imperfect trapping strength and the finite trap size are found to control the early-time behavior, while the trap shape does not much affect the dynamics of the theta distance. A dimensional crossover was found for a perfect trap with a finite radius, when the theta distance was measured from the trap surface. The actual trapping efficiency was determined for different laser powers of the phototrap. Results are supported by analytical equations, exact enumerations, and Monte Carlo simulations.