Structure and diffracted intensity in a model for irreversible island‐forming chemisorption with domain boundaries

Despite the awareness that island‐forming chemisorption is often kinetically limited and intrinsically nonequilibrium, there is little sophisticated analysis of the corresponding island structure or diffracted intensity. Here we analyze a model where species irreversibly and immobilely chemisorb (commensurately) from a precursor source, with distinct rates for island nucleation (chemisorptionin an empty region) and growth (chemisorption at island perimeters), the latter rates being larger. Specifically, we consider the formation of one‐dimensional double‐spaced islands, and two‐dimensional checkerboard C(2×2) islands on a square lattice. In both cases (permanent) domain boundaries form between out‐of‐phase islands. We analyze scaling of the saturation coverage, a characteristiclinear island dimension, spatial correlations, etc., with the ratio of growth to nucleation rates. The structure of individual islands, and of the saturation domain boundary ‘‘network’’ are elucidated. The corresponding diffracted intensity exhibits significant interference at superlattice beams, and diminution at integral order beams as saturation is approached

Competitive irreversible random one-, two-, three-, . . . point adsorption on two-dimensional lattices

An analytic treatment of competitive, irreversible (immobile) random one-, two-, three-, . . . point adsorption (or monomer, dimer, trimer, . . . filling) on infinite, uniform two-dimensional lattices is provided by applying previously developed truncation schemes to the hierarchial form of the appropriate master equations. The behavior of these processes for two competing species is displayed by plotting families of ‘‘filling trajectories’’ in the partial-coverage plane for various ratios of adsorption rates. The time or coverage dependence of various subconfiguration probabilities can also be analyzed. For processes where no one-point (monomer) adsorption occurs, the lattice cannot fill completely; accurate estimates of the total (and partial) saturation coverages can be obtained

Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices

Models where pairs, triples, or larger (typically connected) sets of sites on a 2Dlattice ‘‘fill’’ irreversibly (described here as dimer, trimer, ... filling or adsorption),either randomly or cooperatively, are required to describe many surfaceadsorption and reaction processes. Since filling is assumed to be irreversible and immobile (species are ‘‘frozen’’ once adsorbed), even the stationary, saturation state, which is nontrivial since the lattice cannot fill completely, is not in equilibrium. The kinetics and statistics of these processes are naturally described by recasting the master equations in hierarchic form for probabilities of subconfigurations of empty sites. These hierarchies are infinite for the infinite lattices considered here, but approximate solutions can be obtained by implementing truncation procedures. Those used here exploit a shielding property of suitable walls of empty sites peculiar to irreversible filling processes. Accurate results, including saturation coverage estimates, are presented for random filling of dimers, and trimers of different shapes, on various infinite 2Dlattices, and for square tetramers on an infinite square lattice

Cluster-size distributions for irreversible cooperative filling of lattices. II. Exact one-dimensional results for noncoalescing clusters

We consider processes where the sites of an infinite, uniform, one-dimensional lattice are filled irreversibly and cooperatively, with the rates ki, depending on the number i=0,1,2 of filled nearest neighbors. Furthermore, we suppose that filling of sites with both neighbors already filled is forbidden,so k2=0. Thus, clusters can nucleate and grow, but cannot coalesce. Exact truncation solutions of the corresponding infinite hierarchy of rate equations for subconfiguration probabilities are possible. For the probabilities of filled s-tuples fs as a function of coverage, θ≡f1, we find that fs/fs+1=D(θ)s+C(θ,s), where C(θ,s)/s→0 as s→∞. This corresponds to faster than exponential decay. Also, if ρ≡k1/k0, then one has D(θ)∼(2ρθ)−1 as θ→0. The filled-cluster-size distribution ns has the same characteristics. Motivated by the behavior of these families of fs/fs+1-vs-s curves, we develop the natural extension of fs to s≤0. Explicit values for fs and related quantities for ‘‘almost random’’ filling, k0=k1, are obtained from a direct statistical analysis

Inequivalent models of irreversible dimer filling: ‘‘Transition state’’ dependence

Irreversible adsorption of diatomics on crystalline surfaces is sometimes modeled as random dimer filling of adjacent pairs of sites on a lattice. We note that this process can be implemented in two distinct ways: (i) randomly pick adjacent pairs of sites,  jj’, and fill  jj’ only if both are empty (horizontal transition state); or (ii) randomly pick a single site,  j, and if  j and at least one neighbor are empty, then fill  j and a randomly chosen empty neighbor (vertical transition state). Here it is instructive to consider processes which also include competitive random monomer filling of single sites. We find that although saturation (partial) coverages differ little between the models for pure dimer filling, there is a significant difference for comparable monomer and dimer filling rates. We present exact results for saturation coverage behavior for a linear lattice, and estimates for a square lattice. Ramifications for simple models of CO oxidation on surfaces are indicated

Random walks on finite lattices with multiple traps: Application to particle-cluster aggregation

For random walks on finite lattices with multiple (completely adsorbing) traps, one is interested in the mean walk length until trapping and in the probability of capture for the various traps (either for a walk with a specific starting site, or for an average over all nontrap sites). We develop the formulation of Montroll to enable determination of the large-lattice-size asymptotic behavior of these quantities. (Only the case of a single trap has been analyzed in detail previously.) Explicit results are given for the case of symmetric nearest-neighbor random walks on two-dimensional (2D) square and triangular lattices. Procedures for exact calculation of walk lengths on a finite lattice with a single trap are extended to the multiple-trap case to determine all the above quantities. We examine convergence to asymptotic behavior as the lattice size increases. Connection with Witten-Sander irreversible particle-cluster aggregation is made by noting that this process corresponds to designating all sites adjacent to the cluster as traps. Thus capture probabilities for different traps determine the proportions of the various shaped clusters formed. (Reciprocals of) associated average walk lengths relate to rates for various irreversible aggregation processes involving a gas of walkers and clusters. Results are also presented for some of these quantities

Hazards to golden-mantled ground squirrels and associated secondary hazard potential from strychnine baiting for forest pocket gophers

Radio telemetry and capture-recapture techniques were used to evaluate the hazards to golden-mantled ground squirrels (Spermophilus lateralis) from hand baiting with 0.5% strychnine-treated oats for western pocket gophers (Thomomys mazama) on conifer plantations in eastern Oregon. Toxicology data were collected on field-killed and caged ground squirrels and on caged mink (Mustela vison), great horned owls (Bubo virginianus), and red-tailed hawks (Buteo jamaicensis). Ground squirrel populations were reduced 50 to 75% following underground baiting for pocket gophers. Maximum amount of strychnine alkaloid found in cheek pouches and carcass of a field-killed golden-mantled ground squirrel was 2.88 mg. Mean amount of strychnine in carcasses was 0.35 mg; almost all occurred in the gut. The estimated LD50 for mink was 0.6 mg/kg. The lowest lethal dose for great horned owls and red-tailed hawks was 7.7 mg/kg and 10.2 mg/kg, respectively. The LD50 for owls and hawks was not determined. Long-term effects on golden-mantled ground squirrel populations and secondary hazard potential to owls and hawks were judged to be minimal. Wild mustelids as large as mink could be adversely affected by consuming the gut content of strychnine-killed golden-mantled ground squirrels

Modeling spatiotemporal behavior of the NO+CO reaction on Pt

Various features of NO+CO reaction kinetics on Pt(100) surfaces, including temporal oscillations, are well described by a three‐variable model incorporating only the CO, NO, and O coverages. Here we analyze the corresponding reaction–diffusion equations demonstrating the existence of chemical waves where an ‘‘oscillating phase’’ displaces an unreactive NO/CO phase leaving a spatially periodic structure in its wake; pulses excited via inhomogeneities from an unreactive NO/CO background; and Turing structures for sufficiently unequal NO and CO diffusion rates

Cluster-size distributions for irreversible cooperative filling of lattices. I. Exact one-dimensional results for coalescing clusters

We consider processes where the sites of an infinite, uniform lattice are filled irreversibly and cooperatively, with the rate of adsorption at a site depending on the state of its nearest neighbors (only). The asymmetry between empty and filled sites, associated with irreversibility, leads one to consider the closed infinite coupled hierarchies of rate equations for probabilities of connected and singly, doubly, etc., disconnected empty subconfigurations and results in an empty-site-shielding property. The latter allows exact solutions, via truncation, of these equations in one dimension and is used here to determine probabilities of filled s-tuples, fs (f1≡θ is the coverage), and thus of clusters of exactly s filled sites, ns≡fs-2fs+1+fs+2 for s≤13 and 11, respectively. When all rates are nonzero so that clusters can coalesce, the fs and ns distributions decay exponentially as s→∞, and we can accurately estimate the asymptotic decay rate λ(θ)≡ lims→∞ fs+1/fs≡ lims→∞ ns+1/ns, where 0=λ(0)≤λ(θ)≤λ(1)=1. Divergent behavior of the average cluster size, as θ→1, is also considered. In addition, we develop a novel technique to determine directly the asymptotic decay rate λ(θ) and indicate its extension to higher-dimensional irreversible cooperative filling (and to other dynamic processes on lattices)

The multicommodity assignment problem: a network aggregation heuristic

AbstractWe present a network-based heuristic procedure for solving a class of large non-unimodular assignment-type problems. The procedure is developed from certain results concerning multi-commodity network flows and concepts of node-aggregation in networks. Computational experience indicates that problems with over fifteen thousand integer variables can be solved in well under ten seconds using state-of-the-art network optimization software