Exact results for the reactivity of a single-file system

We derive analytical expressions for the reactivity of a Single-File System with fast diffusion and adsorption and desorption at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of adsorption and desorption. For large systems the number of nonconverted particles decreases exponentially with distance from the adsorption/desorption end.Comment: 4 pages, 2 figure

Steady-State Properties of Single-File Systems with Conversion

We have used Monte-Carlo methods and analytical techniques to investigate the influence of the characteristic parameters, such as pipe length, diffusion, adsorption, desorption and reaction rate constants on the steady-state properties of Single-File Systems with a reaction. We looked at cases when all the sites are reactive and when only some of them are reactive. Comparisons between Mean-Field predictions and Monte-Carlo simulations for the occupancy profiles and reactivity are made. Substantial differences between Mean-Field and the simulations are found when rates of diffusion are high. Mean-Field results only include Single-File behavior by changing the diffusion rate constant, but it effectively allows passing of particles. Reactivity converges to a limit value if more reactive sites are added: sites in the middle of the system have little or no effect on the kinetics. Occupancy profiles show approximately exponential behavior from the ends to the middle of the system.Comment: 15 pages, 20 figure

Electromigration of Single-Layer Clusters

Single-layer atom or vacancy clusters in the presence of electromigration are studied theoretically assuming an isotropic medium. A variety of distinctive behaviors distinguish the response in the three standard limiting cases of periphery diffusion (PD), terrace diffusion (TD), and evaporation-condensation (EC). A general model provides power laws describing the size dependence of the drift velocity in these limits, consistent with established results in the case of PD. The validity of the widely used quasistatic limit is calculated. Atom and vacancy clusters drift in opposite directions in the PD limit but in the same direction otherwise. In absence of PD, linear stability analysis reveals a new type of morphological instability, not leading to island break-down. For strong electromigration, Monte Carlo simulations show that clusters then destabilize into slits, in contrast to splitting in the PD limit. Electromigration affects the diffusion coefficient of the cluster and morphological fluctuations, the latter diverging at the instability threshold. An instrinsic attachment-detachment bias displays the same scaling signature as PD in the drift velocity.Comment: 11 pages, 4 figure

Equilibrium Properties of A Monomer-Monomer Catalytic Reaction on A One-Dimensional Chain

We study the equilibrium properties of a lattice-gas model of an $A + B \to 0$ catalytic reaction on a one-dimensional chain in contact with a reservoir for the particles. The particles of species $A$ and $B$ are in thermal contact with their vapor phases acting as reservoirs, i.e., they may adsorb onto empty lattice sites and may desorb from the lattice. If adsorbed $A$ and $B$ particles appear at neighboring lattice sites they instantaneously react and both desorb. For this model of a catalytic reaction in the adsorption-controlled limit, we derive analytically the expression of the pressure and present exact results for the mean densities of particles and for the compressibilities of the adsorbate as function of the chemical potentials of the two species.Comment: 19 pages, 5 figures, submitted to Phys. Rev.

Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.Comment: AMSTeX, 27 pages + 4 figure

Correlation effects in diffusion of CH4/CF4 mixtures in MFI zeolite. A study linking MD simulations with the Maxwell-Stefan formulation

Correlation effects in diffusion of CH<SUB>4 </SUB>and CF<SUB>4</SUB> in MFI zeolite have been investigated with the help of molecular dynamics (MD) simulations and the Maxwell-Stefan (M-S) formulation. For single-component diffusion, the correlations are captured by the self-exchange coefficient &#208; <SUP>corr</SUP><SUB> ii</SUB>; in the published literature this coefficient has been assumed to be equal to the single-component M-S diffusivity, &#208;<SUB>i</SUB>. A detailed analysis of single-component diffusivity data from MD, along with published kinetic Monte Carlo (KMC) simulations, reveals that &#208; <SUP>corr</SUP><SUB> ii</SUB>;/&#208; <SUB>i </SUB>is a decreasing function of the molecular loading, depends on the guest-host combination, and is affected by intermolecular repulsion (attraction) forces. A comparison of published KMC simulations for diffusion of various molecules in MFI, with those of primitive square and cubic lattices, shows that the self-exchange coefficient increases with increasing connectivity. Correlations in CH<SUB>4</SUB>/CF<SUB>4</SUB> binary mixtures are described by the binary exchange coefficient &#208; <SUP>corr</SUP><SUB>12</SUB>; this exchange coefficient has been examined using Onsager transport coefficients computed from MD simulations. Analysis of the MD data leads to the development of a logarithmic interpolation formula to relate &#208; <SUP>corr</SUP><SUB>12</SUB>; with the self-exchange coefficient &#208; <SUP>corr</SUP><SUB>12</SUB>; of the constituents. The suggested procedure for estimation of &#208; <SUP>corr</SUP><SUB>12</SUB>; is validated by comparison with MD simulations of the Onsager and Fick transport coefficients for a variety of loadings and compositions. Our studies show that a combination of the M-S formulation and the ideal adsorbed solution theory allows good predictions of binary mixture transport on the basis of only pure component diffusion and sorption data