Long-time Kinetics Research Articles

Adsorption-desorption model and its application to vibrated granular materials.

We investigate both analytically and by numerical simulation the kinetics of a microscopic model of hard rods adsorbing on a linear substrate, a model that is relevant for compaction of granular materials. The computer simulations use an event-driven algorithm that is particularly efficient at very long times. For a small, but finite desorption rate, the system reaches an equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as 1/t, a logarithmic one where the density varies as 1/ln(t), followed by a terminal exponential approach. The characteristic relaxation time of the final regime, though incorrectly predicted by mean field arguments, can be obtained with a systematic gap-distribution approach. The density fluctuations at equilibrium are also investigated, and the associated time-dependent correlation function exhibits a power law regime followed by a final exponential decay. Finally, we show that denser particle packings can be obtained by varying the desorption rate during the process.

Sluggish kinetics in the parking lot model

We investigate, both analytically and by computer simulation, the kinetics of a microscopic model of hard rods adsorbing on a linear substrate. For a small, but finite desorption rate, the system reaches the equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as , a logarithmic one where the density varies as , followed by a terminal exponential approach. A mean-field approach fails to predict the relaxation rate associated with the latter. We show that the correct answer can only be provided by using a systematic description based on a gap-distribution approach.

Adsorption of Charged Latex Particles on Mica Studied by Atomic Force Microscopy

Atomic force microscopy (AFM) is used to study the localized adsorption of charged latex particles onto a mica substrate with varying adsorption times and solution ionic strengths. Images are obtained by employing tapping mode AFM with silane-treated probes to reduce the intrusive effect of the imaging process on physisorbed particles. The initial kinetics of the adsorption process are found to be diffusion-limited and the long-time asymptotic kinetics are found to resemble those of a random sequential adsorption process. Double-layer screening of interparticle electrostatic repulsions is shown to have a controlling effect on the surface coverage at saturation and, to a lesser degree, on the diffusion-limited rate of adsorption.In situimages of adsorbed layers are compared with those of dried samples to reveal the morphological effects of film evaporation on the microstructure of adsorbed particles. Results show that particles in adsorbed layers of high surface coverage can rearrange into two-dimensional clusters during film evaporation—a phenomenon attributed to capillary forces between particles in near contact. Ordering of particles at the solid–liquid interface is analyzed using two-dimensional radial distribution functions. A high degree of short-range order is found among adsorbed particles when the surface coverage approaches saturation, and a significant reduction in the range of ordering due to double-layer screening of interparticle repulsions is also reflected in the radial distributions.

Carrier transfer in inhomogeneous media

From four non-stochastic rigorous theories leading to a set of equations for site-diagonal as well as site off-diagonal elements of the electron (carrier) density matrix (Time-Convolution Generalized Master Equation, Mori theory, Time-Convolutionless Generalized Master Equation and Tokuyama-Mori), the first two (time nonlocal) approaches were recently found to be disabled in the second order in the carrier-bath coupling. On the other hand, the latter two (time local) theories are argued here to lead, in the above order and any electronic system with a site-local coupling to bath, to completely identical and physically fully acceptable equations. The theory is applied to a periodic chain and asymmetric dimer. It is shown that, irrespective of problems with introducing γmn or γmn(m≠n) Haken-Strobl-Reineker parameters, the usual transition from the non-activated to activated (Arrhenius-type) ‘up-and-down’ asymmetric Marcus long-time reaction kinetics is obtained. The usual long-time markovian description of the population kinetics assumed in the standard theory is, however, found to be unjustified.

Polyexponential kinetics of chemical reactions in condensed media within the quasiclassical approximation

Polyexponential kinetical behavior typical for condensed phase reactions in highly viscous media is studied on a simple example of one-dimensional diffusion equation with a sink modeling a chemical conversion of reactants. The corresponding polyexponential regime is demonstrated to have a thorough analogy with the quasiclassical approximation of one-dimensional quantum mechanics and a relevant approximation for the Green’s function is developed. The asymptotic short- and long-time kinetics are examined at the analytical level. Contrary to the frozen medium approximation according to which the slow diffusion motion of the medium is entirely ignored, the present quasiclassical model is fit for a qualitative description of the total time interval covering the reaction events from the initial moment up to the ultimate steady-state monoexponential evolution. The range of validity of the quasiclassical approach is discussed. Numerical tests expose some peculiarities of the present treatment for equilibrium and nonequilibrium initial distributions. The work presents a qualitative development of the theory of nonexponential kinetics pioneered by papers of Agmon and Hopfield, Sumi and Marcus, and Nadler and Marcus.

Competitive reversible binding: A theoretical study of density effects on the long-time relaxation

Competitive reversible binding is studied for a one-dimensional continuum model. Taking the reaction as a stochastic two-state process (free or occupied binding site), from many-body equations by superposition a closed system of three coupled reactive equations is derived. Linearized versions of these equations are used to get low density approximations for the long-time kinetics. Starting point is an approximation (a) from which a Szabo–Zwanzig type t−1/2 long-time law can be followed. On the basis of an approximate relation between the state-specific distribution functions obtained in (a), a higher order in density approximation (b) is derived which prescribes a concentration effect on the long-time kinetics. According to (b) the t−1/2 law is also asymptotically valid for t→∞, but with a different concentration-dependent amplitude. For time windows in an intermediate long-time range the relaxation to equilibrium appears as satisfying a modified power law (∝ t−α with α≠1/2). These analytic results, which are interesting with respect to deviations from a predicted t−3/2 decay law observed for photoexcited proton transfer in water [D. Huppert et al., Phys. Rev. Lett. 68, 3932 (1992)], are related to recent Brownian simulations of the pseudounimolecular reaction.

Cage Effect on the Diffusion-Controlled Recombination Kinetics

The effect of the spherically symmetric caging field on the asymptotic time behavior of the geminate recombination (GR) kinetics is explored. Time-dependent solution of the Smoluchowski equation with the Coulomb potential and the spherically symmetric linear caging potential is derived. The asymptotic kinetics is characterized by the nonuniversal exponent, which increases linearly with the field for weak fields. The deviation from the universal diffusion-controlled kinetics k(t)∼t -3/2 is due to the «finite volume» effects. The model can mimic the many-body effects on GR kinetics. Its possible use for the interpretation of the recent experimental data on the pH effect on the long-time GR kinetics is discussed

Stochastic analysis of the asymptotic kinetics of multi-particle spurs

Analyses are presented of the long-time asymptotic kinetics of spur reactions in the absence of scavenger, and of the asymptotic concentration dependence of the scavenging yield. The results show no dependence on the initial spatial distribution of the particles apart from that inherent in the escape yield. However, the asymptotics are shown to provide further information about the probability distribution of the numbers of particles escaping, and hence to provide an indirect probe of the initial number distribution.

Asymptotic results for the random sequential addition of unoriented objects.

Asymptotic kinetics for random sequential addition of unoriented nonspherical objects is characterized by an algebraic time dependence. By studying 1D systems, we show that the exponents describing the random sequential addition of objects with and without proper area are not simply related: Whereas the asymptotic behavior for rectangles follows the expected ${\mathit{t}}^{\mathrm{\ensuremath{-}}1/2}$ law, the long-time kinetics for infinitely thin line segments is governed by a nontrivial, irrational, exponent (${\mathit{t}}^{\mathrm{\ensuremath{\surd}}2\mathrm{\ensuremath{-}}1}$) which results from a competition between creation and destruction of targets in the asymptotic regime.

On the reversible long-time kinetics of the magnetic permeability relaxation in amorphous ferromagnets: New investigations

Abstract Long-term investigations of the time decay of the reversible magnetic permeability of two soft ferromagnetic amorphous alloys have been performed at room temperature over the extended time interval 10−4–106s. The involved processes of directional ordering are characterized by a wide distribution of activation energies. The activation energy spectrum has been analysed using the canonical Primak procedure. A suitable experimental method, allowing one to interface directly with the kinetics of the atomic ordering events, is proposed for investigating the validity of the current model of independent ordering processes.

Fluctuation-induced kinetics of reversible coagulation

The influence of spatial fluctuations in the density of monomeric units on the long-time kinetics of reversible coagulation is investigated. It is shown that the long-time approach to the equilibrium cluster size distribution is determined by relaxation of the spatial fluctuation spectrum and described by a power-law dependence.

Corrosion of austenitic and martensitic stainless steels in flowing 17Li-83Pb alloy

With regard to the behaviour of 316 L stainless steel at 400°C in flowing anisothermal 17Li-83Pb the mass transfer suffered by this steel appears to be quite important without noticeable influence of constant or cyclic stress. Evaluation made from solution-annealed specimens leads to a corrosion rate of approximately 30 μm yr−1 at steady state to which a depth of 25 μm has to be added to take into account the initial period phenomena. On the other hand, with semi-stagnant 17Li-83Pb at 400° C, the mass transfer of 316 L steel appears to be lower and more acceptable after a 3000-h exposure; but long-time kinetics data have to be achieved in order to see if that better behaviour is persistent and does not correspond to a longer incubation period. As for the martensitic steels their corrosion rate at 450°C in the thermal convection loop TULIP is constant up to 3000 h and five times lower than that observed for 316 L steel in the same conditions.

Hydrogenation and annealing kinetics of group-III acceptors in oxidized silicon exposed to keV electrons

Group-III acceptors are deactivated by hydrogen released by 8 keV electrons in metal-oxide-silicon capacitors. The decay of the acceptor density during keV electron beam irradiation shows three conjoined phases: an initial delay, a short-time transient, and a long-time transient. This overlapping temporal characteristic is related to comparable rates of hydrogen bond breaking at the gate–oxide interface, hydrogen migration across the oxide, and emission and capture of proton at the group-III acceptor. Isothermal annealing data showed clearly two distinct annealing phases: an initial exponential rise and the long-time second-order recovery kinetics. The hydrogenation and annealing rate coefficients from these electron beam irradiated oxides are different from those obtained from avalanche electron injection (AEI) experiments. The difference suggests that the atomic structure surrounding the hydrogen-acceptor complex depends on the hydrogenation energetics. Compared with those electrons in the AEI experiments (tens eV), the higher-energy (keV) electrons can create more extended interfacial dangling bonds which are hydrogen or proton traps.

Experimental Study of Ordering Kinetics in a Highly Degenerate Superlattice

The evolution of domain ordering is studied with use of real-time x-ray scattering in stage-2, -4, and -6 Sb${\mathrm{Cl}}_{5}$-intercalated graphite, an experimental realization of a fourteen-state quasi two-dimensional superlattice. Quenching from the disordered phase reveals scaling behavior $L\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}=0.52\ifmmode\pm\else\textpm\fi{}0.05$. Evidence for defect pinning is observed, leading to very sluggish long-time kinetics. The experimental findings are discussed in terms of recent theoretical predictions and Monte Carlo simulations of highly degenerate systems.

Simulation calculations of the charge carrier transport in polyethylene

The prerequisites for simulating the charge transport by MONTE CARLO methods are summarized and tested by experiment with PE. For this simulation calculations space charges have to be considered, particularly in interpreting the long-time kinetics. For them MONTE CARLO methods were found to be insufficient. In investigating the long-time kinetics by surface potential measurements deviations from the dispersive behaviour were observed.

Effect of reagent density fluctuations on bimolecular reaction kinetics

The peculiarities of the kinetics of a bimolecular reaction A + B → C caused by non-Poisson fluctuations of reagent densities spontaneously produced during a diffusion-controlled reaction are analysed. The asymptotic long-time kinetics is predicted to be n ∝ t − 3 4 (for equal reagent concentrations) contrary to the ordinary law of formal chemical kinetics n ∝ t − t .

Kinetics of a Square Cascade of Close-Separation Stages under Total Reflux

Abstract To facilitate the determination of the separation factor and the number of theoretical stages of a square cascade of close-separation stages from measurements of its long-time kinetics under total reflux, extensive tables of kinetics parameters have been produced in accordance with K. Cohen's theory. Cohen's treatment has been extended in several ways. The kinetics parameters of the first transient term have been finely mapped, and the ranges of various parameters have been extended to include large overall separations as well as the stripping section. The second transient term of the long-time kinetics has been evaluated, and a possible application of this correction term has been suggested in relation to the experimental determination of the column parameters. Under comparable conditions a steady concentration profile, along the column, is attained faster in the stripping section than in the enriching section. A distinction between the enriching and stripping section is important in using the transient theory for the evaluation of the cascade characteristics under ordinary laboratory conditions.