Irreversible random sequential adsorption (RSA) on lattices, and continuum "car parking" analogues, have long received attention as models for reactions on polymer chains, chemisorption on single-crystal surfaces, adsorption in colloidal systems, and solid state transformations. Cooperative generalizations of these models (CSA) are sometimes more appropriate, and can exhibit richer kinetics and spatial structure, e.g., autocatalysis and clustering. The distribution of filled or transformed sites in RSA and CSA is not described by an equilibrium Gibbs measure. This is the case even for the saturation "jammed" state of models where the lattice or space cannot fill completely. However exact analysis is often possible in one dimension, and a variety of powerful analytic methods have been developed for higher dimensional models. Here we review the detailed understanding of asymptotic kinetics, spatial correlations, percolative structure, etc., which is emerging for these far-from-equilibrium processes.

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We examine the competition between diffusion-mediated irreversible nucleation and growth of islands during submonolayer deposition on perfect substrates. We provide a detailed scaling theory for the complete distribution of island sizes and separations, both with the ratio of diffusion to deposition rate and with time. Scaling functions and exponents are obtained by simulation. The leading scaling behavior is independent of details of the island structure. These results are supplemented by an analysis of rate equations for the islandsize distribution whose unconventional form appropriately describes island nucleation and growth mechanisms. The exponents agree with the simulations and the island-size distribution shows qualitative agreement. We further provide simulation results for the scaling of the island-separation distribution, quantifying, in particular, the depletion in the concentration of pairs of islands at small separations. Disciplines Condensed Matter Physics | Physics Comments This article is published as Bartelt, M. C., and J. W. Evans. "Scaling analysis of diffusion-mediated island growth in surface adsorption processes."

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Scanning tunneling microscopy shows that large two-dimensional Ag clusters on Ag(100) can diffuse. The value of the diffusion coefficient at room temperature is of order 10-17 cm2s-1 and varies little, if at all, with cluster size in the range studied, 100 to 720 atoms per cluster. This weak variation rules out periphery diffusion as the main mechanism of cluster diffusion, suggesting instead two-dimensional evaporationcondensation. This conclusion is compatible with the energetics of atomic-scale events within the cluster and with the dissolution of small clusters observed at low coverages. Keywords Ames Laboratory, Mathematics Disciplines Mathematics | Physical Chemistry CommentsThis article is from Physical Review Letters 73, no. 19 (1994) .- (a) . (

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We describe experimental observations and theoretical analysis of the coarsening of distributions of twodimensional nanoclusters, either adatom islands or vacancy pits, on metal surfaces. A detailed analyses is provided for Ag(111) and Ag(100) surfaces, although we also discuss corresponding behavior for Cu(111) and Cu(100) surfaces. The dominant kinetic pathway for coarsening can be either Ostwald ripening (OR), i.e., growth of larger clusters at the expense of smaller ones, or Smoluchowski ripening (SR), i.e., diffusion and coalescence of clusters. First, for pristine additive-free surfaces, we elucidate the factors which control the dominant pathway. OR kinetics generally follows the predictions of mesoscale continuum theories. SR kinetics is controlled by the size-dependence of cluster diffusion. However, this size-dependence, together with that of nanostructure shape relaxation upon coalescence, often deviates from mesoscale predictions as a direct consequence of the nanoscale dimension of the clusters. Second, we describe examples for the above systems where trace amounts of a chemical additive lead to dramatic enhancement of coarsening. We focus on the scenario where "facile reaction" of metal and additive atoms leads to the formation of mobile additivemetal complexes which can efficiently transport metal across the surface, i.e., additive-enhanced OR. A suitable reaction-diffusion equation formulation is developed to describe this behavior. ReceiVed: July 19, 2008; ReVised Manuscript ReceiVed: December 25, 2008 We describe experimental observations and theoretical analysis of the coarsening of distributions of twodimensional nanoclusters, either adatom islands or vacancy pits, on metal surfaces. A detailed analyses is provided for Ag(111) and Ag(100) surfaces, although we also discuss corresponding behavior for Cu (111) and Cu(100) surfaces. The dominant kinetic pathway for coarsening can be either Ostwald ripening (OR), i.e., growth of larger clusters at the expense of smaller ones, or Smoluchowski ripening (SR), i.e., diffusion and coalescence of clusters. First, for pristine additive-free surfaces, we elucidate the factors which control the dominant pathway. OR kinetics generally follows the predictions of mesoscale continuum theories. SR kinetics is controlled by the size-dependence of cluster diffusion. However, this size-dependence, together with that of nanostructure shape relaxation upon coalescence, often deviates from mesoscale predictions as a direct consequence of the nanoscale dimension of the clusters. Second, we describe examples for the above systems where trace amounts of a chemical additive lead to dramatic enhancement of coarsening. We focus on the scenario where "facile reaction" of metal and additive atoms leads to the formation of mobile additivemetal complexes which can efficiently transport metal across the surface, i.e., additive-enhanced OR. A suitable reaction-diffusion equation formulation is developed to describe this behavior.

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