Effective Trapping Rate Research Articles

Boundary homogenization for patchy surfaces trapping patchy particles.

Trapping diffusive particles at surfaces is a key step in many systems in chemical and biological physics. Trapping often occurs via reactive patches on the surface and/or the particle. The theory of boundary homogenization has been used in many prior works to estimate the effective trapping rate for such a system in the case that either (i) the surface is patchy and the particle is uniformly reactive or (ii) the particle is patchy and the surface is uniformly reactive. In this paper, we estimate the trapping rate for the case that the surface and the particle are both patchy. In particular, the particle diffuses translationally and rotationally and reacts with the surface when a patch on the particle contacts a patch on the surface. We first formulate a stochastic model and derive a five-dimensional partial differential equation describing the reaction time. We then use matched asymptotic analysis to derive the effective trapping rate, assuming that the patches are roughly evenly distributed and occupy a small fraction of the surface and the particle. This trapping rate involves the electrostatic capacitance of a four-dimensional duocylinder, which we compute using a kinetic Monte Carlo algorithm. We further use Brownian local time theory to derive a simple heuristic estimate of the trapping rate and show that it is remarkably close to the asymptotic estimate. Finally, we develop a kinetic Monte Carlo algorithm to simulate the full stochastic system and then use these simulations to confirm the accuracy of our trapping rate estimates and homogenization theory.

Electrically Tuning Interfacial Ion Redistribution for mica/WSe2 Memory Transistor

AbstractMemory device is an important part of electronic equipment. 2D transition metal dichalcogenides that exhibit novel electrical characteristics hold promise in developing new types of memory device. Here, the memory effect in 2D mica/WSe2 heterostructure is investigated. Under applying constant bias voltage and gate voltage, the K+ ions in mica will migrate in the direction of the electric field and be trapped to enable the memory function. The gradient K+ ions work as long‐range scatters to electrostatically dope the WSe2 channel. The shift of the threshold voltage indicates an electrostatic doping concentration up to 2.11 × 1012 cm−2. The operating voltage is as low as 10 V and the on/off ratio is estimated to be 104. To determine the mechanism, the dynamic behavior of the device is discussed and a model is proposed which reveals the correlation between the programming/erasing process and the device performance. Moreover, through defining and studying the effective charge trapping rate, θ, it is found that the trapped charge is proportional to the charge flowing through the channel which means that the device performance can be finely tuned by the programming process.

Mean first passage time for a particle diffusing on a disk with two absorbing traps at the boundary.

The problem of survival of a Brownian particle diffusing on a disk with a reflective boundary that has two absorbing arcs is treated analytically. The framework of boundary homogenization is applied to calculate the effective trapping rate of the disk boundary, and this enables estimation of the mean first passage time. The method of conformal mapping is applied to transform the original system to a simpler geometrical configuration (a flat reflective boundary with a periodic configuration of identical absorbing strips) for which the analytical solution is known. The expression for the mean first passage time is simplified for some limiting cases (small arc or small gap). The derived analytical expressions compare favorably with the results of Brownian particle simulations and other analytical results from the literature.

Boundary homogenization for trapping patchy particles.

Many systems in chemical and biological physics involve diffusing particles being trapped by absorbing patches on otherwise reflecting surfaces. Such systems are commonly studied by boundary homogenization, in which the heterogenous boundary condition on the patchy surface is replaced by a uniform boundary condition involving a single parameter which encapsulates the effective trapping properties of the surface. In prior works on boundary homogenization, the surface is patchy and the diffusing particles are homogeneous. In this paper, we consider the opposite scenario in which a homogenous surface traps patchy particles, which could model proteins with localized binding sites, cells with membrane receptors, or patchy colloids or nanoparticles. We derive an explicit formula for the effective trapping rate which reveals a fundamental interplay between the translational and rotational diffusivities of the patchy particle, a phenomenon not typically seen in boundary homogenization. Motivated by receptors on the cell membrane, our analysis also allows for the possibility that the patches diffuse on the surface of the particle. We formulate the system in terms of a high-dimensional, time-dependent, anisotropic diffusion equation and employ matched asymptotic analysis to derive the effective trapping rate. We confirm our results by detailed numerical simulations.

Trapping of diffusing particles by short absorbing spikes periodically protruding from reflecting base.

We study trapping of diffusing particles by a periodic non-uniform boundary formed by absorbing spikes protruding from a reflecting flat base. It is argued that such a boundary can be replaced by a flat uniform partially absorbing boundary with a properly chosen effective trapping rate. Assuming that the spikes are short compared to the inter-spike distance, we propose an approximate expression which gives the trapping rate in terms of geometric parameters of the boundary and the particle diffusivity. To validate this result, we compare some theoretical predictions based on the expression for the effective trapping rate with corresponding quantities obtained from Brownian dynamics simulations.

Boundary homogenization for a sphere with an absorbing cap of arbitrary size.

This paper focuses on trapping of diffusing particles by a sphere with an absorbing cap of arbitrary size on the otherwise reflecting surface. We approach the problem using boundary homogenization which is an approximate replacement of non-uniform boundary conditions on the surface of the sphere by an effective uniform boundary condition with appropriately chosen effective trapping rate. One of the main results of our analysis is an expression for the effective trapping rate as a function of the surface fraction occupied by the absorbing cap. As the cap surface fraction increases from zero to unity, the effective trapping rate increases from that for a small absorbing disk on the otherwise reflecting sphere to infinity which corresponds to a perfectly absorbing sphere. The obtained expression for the effective trapping rate is applied to find the rate constant describing trapping of diffusing particles by an absorbing cap on the surface of the sphere. Finally, we find the capacitance of a metal cap of arbitrary size on a dielectric sphere using the relation between the capacitance and the rate constant of the corresponding diffusion-limited reaction. The relative error of our approximate expressions for the rate constant and the capacitance is less than 5% over the entire range of the cap surface fraction from zero to unity.

Trapping of diffusing particles by striped cylindrical surfaces. Boundary homogenization approach.

We study trapping of diffusing particles by a cylindrical surface formed by rolling a flat surface, containing alternating absorbing and reflecting stripes, into a tube. For an arbitrary stripe orientation with respect to the tube axis, this problem is intractable analytically because it requires dealing with non-uniform boundary conditions. To bypass this difficulty, we use a boundary homogenization approach which replaces non-uniform boundary conditions on the tube wall by an effective uniform partially absorbing boundary condition with properly chosen effective trapping rate. We demonstrate that the exact solution for the effective trapping rate, known for a flat, striped surface, works very well when this surface is rolled into a cylindrical tube. This is shown for both internal and external problems, where the particles diffuse inside and outside the striped tube, at three orientations of the stripe direction with respect to the tube axis: (a) perpendicular to the axis, (b) parallel to the axis, and

Time-dependent diffusion in tubes with periodic partitions

The presence of obstacles leads to a slowdown of diffusion. We study the slowdown when diffusion occurs in a tube, and obstacles are periodically spaced identical partitions with circular apertures of arbitrary radius in their centers. The mean squared displacement of a particle diffusing in such a system at large times is given by ⟨Δx2(t)⟩=2Defft, t→∞, where Deff is the effective diffusion coefficient, which is smaller than the particle diffusion coefficient in the tube with no partitions, D0. The latter characterizes the short-time behavior of the mean squared displacement, ⟨Δx2(t)⟩=2D0t, t→0. Thus, the particle diffusion coefficient decreases from D0 to Deff as time goes from zero to infinity. We derive analytical solutions for the Laplace transforms of the time-dependent diffusion coefficient and the mean squared displacement that show how these functions depend on the geometric parameters of the tube. To obtain these solutions we replace nonuniform partitions with apertures by effective partitions that are uniformly permeable for diffusing particles. Our choice of the partition permeability is based on the recent result for the corresponding effective trapping rate obtained by means of boundary homogenization. To establish the range of applicability of our approximate theory we compare its predictions with the results found in Brownian dynamics simulations. Comparison shows excellent agreement between the two at arbitrary value of the aperture radius when the tube radius does not exceed the interpartition distance.

Boundary Homogenization for Periodic Arrays of Absorbers

We introduce a homogenization procedure for reaction-diffusion equations in domains whose boundary consists of small alternating regions with prescribed Dirichlet and Neumann data of comparable areas. The homogenized problem is shown to satisfy an effective Dirichlet boundary condition which depends on the geometry of the small-scale boundary structure. This problem is also related to finding the effective trapping rate for a Brownian particle next to a surface with a periodic array of perfect absorbers. We use the method of optimal geometric grids to numerically solve the unit cell problem of homogenization. The geometric homogenization factor is obtained for a number of cell geometries (stripes, square and hexagonal arrays of disk-shaped absorbers or emitters) as a function of the surface area fraction occupied by the absorbers. Empirical analytical expressions that give excellent fits to data for the entire range of area fractions and correct asymptotic behaviors in the limits of small and large absorber area fractions are proposed.

Influence of the Photosystem I−Light Harvesting Complex I Antenna Domains on Fluorescence Decay

The time-resolved fluorescence decay of plant PSI-LHCI has been analyzed and compared with its component parts, the PSI core and the peripheral antenna LHCI, in an attempt to (i) define the physical domains associated with the multicomponent decay-associated spectra (DAS) and determine the origin of the kinetically slow steps responsible for them, (ii) formulate a clear working hypothesis for the positive decay-associated spectral amplitudes of the two slowest decay components, and (iii) determine the impact of the peripheral antenna complexes (LHCI) on the effective trapping rate for the photosystem. The results for PSI-LHCI indicate that the three exponential component DAS description, previously reported in the literature, is not numerically unique. The fit minimum is rather broad, which necessitated the introduction of other fit criteria in addition to the purely numerical one. The analysis demonstrates that (i) the physical domains associated with the multicomponent decay are associated with the antenna and particularly with the low-energy spectral forms, (ii) the positive DAS amplitudes of the two slowest decay components are suggested to be due to energy transfer kinetic heterogeneity to different F735 low-energy forms, and (iii) the peripheral antenna slows down the effective photosystem photochemical rate by about 3 times, and this is approximately half due to antenna degeneracy and half due to the low-energy forms.

Homogenization of boundary conditions for surfaces with regular arrays of traps

The problem of trapping of diffusing particles by nonoverlapping absorbing patches randomly or regularly located on a surface arises in numerous settings. Examples include diffusion current to ensembles of microelectrodes, ligand binding to cells, mass transfer to heterogeneous surfaces, ligand accumulation in cell culture assays, etc. see Refs. 1–15 and references therein . The problem is extremely complicated because the boundary conditions on the surface are nonuniform: absorbing on the patches and reflecting otherwise. There is, however, an approximation that greatly simplifies the analysis when the layer of medium above the surface is sufficiently thick. The approximation is based on the fact that, far from the surface, fluxes and concentrations become uniform in the lateral direction and, therefore, indistinguishable from those in the case of uniformly absorbing surface. Keeping this in mind, one can replace the nonuniform boundary conditions on the surface by a uniform radiationtype boundary condition with a properly chosen trapping rate see e.g., Ref. 16 and references therein . We have demonstrated how this procedure works in the case of randomly distributed traps in Refs. 17 and 18. Here we consider the problem with traps regularly distributed over the surface. Our aim is to predict the dependence of on the trap concentration and parameters of the traps and diffusing particles over the entire concentration range. At low concentrations is equal to the product of the concentration and the trapping rate constant of an isolated trap. It turns out that the low-concentration linear dependence of on the trap concentration fails very early, and grows with the concentration much faster even when only a small fraction of the surface is covered by the traps. This happens because “interaction” between traps decays very slowly, as 1 /L, where L is the intertrap distance. As a consequence, collective effects due to this interaction, which lead to the enhancement of the trapping rate, manifest themselves already at low concentrations. In Ref. 17 we reported a boundary homogenization approach for surfaces randomly covered by nonoverlapping circular traps. To describe the enhancement of the trapping rate compared to the linear regime, we introduced the function F of the trap surface fraction and suggested an approximate formula for this function. In Ref. 18 we found that the enhancement due to the collective effects was insensitive to whether the traps were identical or polydisperse and their radii are allowed to fluctuate. This suggests that the enhancement depends only on and is weakly sensitive to the details of the trap arrangement on the surface. To check this hypothesis here we study homogenization of boundaries with regular arrangements of identical traps. Our results support this hypothesis. We find that the values of for the three different arrangements and for random distribution of traps are close to each other the difference is within 20% . In addition, here we study homogenization of periodic nonuniform boundaries formed by alternating absorbing and reflecting stripes. Such boundaries are special because the conventional ideology based on the existence of a trivial limiting behavior of when →0 fails in this case since a stationary flux to an isolated absorbing strip does not exist. Nevertheless, we are able to overcome this difficulty and find the effective trapping rate for such a boundary. In our analysis we use the computer-assisted boundary homogenization approach suggested in Ref. 17: First, based on the limiting behavior and dimensional arguments we express in terms of an unknown dimensionless function of the dimensionless trap surface fraction ,F . We then determine this function using the dependence , which is found by Brownian dynamics simulations as described in Ref. 17 or by solving THE JOURNAL OF CHEMICAL PHYSICS 124, 1 2006

The effect of outer antenna complexes on the photochemical trapping rate in barley thylakoid Photosystem II

We have investigated the previous suggestions in the literature that the outer antenna of Photosystem II of barley does not influence the effective photosystem primary photochemical trapping rate. It is shown by steady state fluorescence measurements at the F 0 fluorescence level of wild type and the chlorina f2 mutant, using the chlorophyll b fluorescence as a marker, that the outer antenna is thermally equilibrated with the core pigments, at room temperature, under conditions of photochemical trapping. This is in contrast with the conclusions of the earlier studies in which it was suggested that energy was transferred rapidly and irreversibly from the outer antenna to the Photosystem II core. Furthermore, the effective trapping time, determined by single photon counting, time-resolved measurements, was shown to increase from 0.17±0.017 ns in the chlorina Photosystem II core to a value within the range 0.42±0.036–0.47±0.044 ns for the wild-type Photosystem II with the outer antenna system. This 2.5–2.8-fold increase in the effective trapping time is, however, significantly less than that expected for a thermalised system. The data can be explained in terms of the outer antenna increasing the primary charge separation rate by about 50%.

Boundary homogenization for trapping by patchy surfaces

We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations. (c) 2004 American Institute of Physics.

Excitation migration and transfer to interstitial traps — low dimensional transport and conformational motion

An effective medium approximation (EMA) has been used in an attempt to analyze incoherent migrational trapping in a system of 1-D regular and immobile donors, where trapping is a time-dependent stochastic process — due to the dynamic conformational disorder of interstitial acceptors. By assuming (I) the time duration of the elementary act of conformational transition to be longer than the time involved in the electronic site-to-site transfer and (II) the transport of excitation during conformational event to be negligible, the hypersurface of the effective trapping rate coefficient K eff ( z ) in Laplace space can be formulated on the basis of a stochastic master equation analysis. The computation has been centered on conformational transitions between two relative positions in the donor-acceptor pair connected by flexible carboncarbon spacer-groups, where the dynamical fluctuation of acceptor positions, due to the conformational motion of spacer segments, dichotomically modulates the trapping rate coefficient. On these premises K eff ( z ) can be obtained by numerically solving a third order polynomial equation which allows, after Laplace inversion, the mean-square distance of migrating excitation 〈 r 2 ( t )〉 and the survival probability of donor excitation 〈 P ( t )〉 to be analyzed. The effect of conformational motion on the excitation trapping efficiency has been calculated for a series of conformative and electronic parameters. The non-Markovian character of trapping becomes apparent for slow to moderate conformational motion in the short-to-intermediate time regime and disappears for fast conformational transitions. Furthermore, the asymptotic trapping rate K eff ( z = 0 + ) which represents the Markov approximation of the memory function K eff ( t ) has been analyzed for different rates of conformational motion and equilibrium conformational probabilities and, finally, the investigation has been extended to 2-D transport in a preliminary attempt.

The role of epitaxy in superconducting tunnel junction detectors

We have experimentally analysed the use of epitaxial and polycrystalline tantalum trapping layers in tunnel junction detectors, using epitaxial niobium based double tunnel junction devices. We have shown that the trapping rate is enhanced by having a low mean-free-path in the Ta trap film and an epitaxial Nb absorber film. This effectively increases the proportion of time spent by a quasiparticle in the trap film. Phonon-quasiparticle scattering, which reduces the effective trapping rate, has been observed.

Temperature Dependence of Positron Trappingto Dislocations in Aluminum

Doppler-broadening lineshapes of positron annihilation in high purity aluminum have been measured as a function of temperature between 4.2 and 275 K after deformation and recovery at room temperature. The effective trapping rate exhibits a strongly negative dependence on temperature below 200 K in material of 99.9999% purity, but only below 70 K in 99.999% purity. The results can be explained with a model where positrons become trapped in deep traps ( e.g. , jogs) via shallow traps (dislocation lines) from which thermal detrapping can occur. The temperature dependence of the effective trapping rate found in material of 99.999% purity is attributed to the temperature dependence of the specific trapping rate to the dislocation line.

Trapping and flow among random arrays of oriented spheroidal inclusions

The effective trapping rate k associated with diffusion-controlled reactions among random distributions of spatially correlated and uncorrelated, oriented spheroidal traps of aspect ratio ε is determined from Brownian motion simulations. Data for k are obtained for prolate cases (ε=2, 5, and 10), oblate cases (ε=0.1, 0.2, and 0.5), and spheres (ε=1) over a wide range of trap volume fractions (φ2) and satisfy recently obtained rigorous lower bounds on k for this statistically anisotropic model. The results for the trapping rate for correlated traps always bounds from above corresponding results for uncorrelated traps. Generally, the trapping rate k, for fixed φ2, increases with decreasing aspect ratio ε, showing a precipitous rise in k as the spheroids become disklike. Using a recent theorem due to Torquato [Phys. Rev. Lett. 64, 2644 (1990)], data for the trapping rate k can be employed to infer information about the fluid permeability tensor K associated with slow viscous flow through porous media composed of the same arrays of oriented spheroidal particles.