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

Journal Article · Sat Jun 01 04:00:00 EDT 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.31.3820· OSTI ID:5761754

Nord, R S; Hoffman, D K; Evans, J W

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, f/sub s/ (f/sub 1/equivalenttheta is the coverage), and thus of clusters of exactly s filled sites, n/sub s/equivalentf/sub s/-2f/sub s+1/+f/sub s+2/ for s< or =13 and 11, respectively. When all rates are nonzero so that clusters can coalesce, the f/sub s/ and n/sub s/ distributions decay exponentially as s..-->..infinity, and we can accurately estimate the asymptotic decay rate lambda(theta)equivalent lim/sub s/..-->..infinity f/sub s+1//f/sub s/equivalent lim/sub s/..-->..infinity n/sub s+1//n/sub s/, where 0 = lambda(0)< or =lambda(theta)< or =lambda(1) = 1. Divergent behavior of the average cluster size, as theta..-->..1, is also considered.

• Research Organization: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 5761754
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 31:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics &amp; Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADSORPTION
AGGLOMERATION
EQUATIONS
IRREVERSIBLE PROCESSES
KINETIC EQUATIONS
KINETICS
LATTICE PARAMETERS
POLYMERS
REACTION KINETICS
SOLID CLUSTERS
SORPTION