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

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

DOI:https://doi.org/10.1103/PhysRevA.31.3831· OSTI ID:5539827

Evans, J W; Nord, R S

We consider processes where the sites of an infinite, uniform, one-dimensional lattice are filled irreversibly and cooperatively, with the rates k/sub i/, 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 k/sub 2/ = 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 f/sub s/ as a function of coverage, thetaequivalentf/sub 1/, we find that f/sub s//f/sub s+1/ = D(theta)s+C(theta,s), where C(theta,s)/s..-->..0 as s..-->..infinity. This corresponds to faster than exponential decay. Also, if rhoequivalentk/sub 1//k/sub 0/, then one has D(theta)approx.(2rhotheta)/sup -1/ as theta..-->..0. The filled-cluster-size distribution n/sub s/ has the same characteristics. Motivated by the behavior of these families of f/sub s//f/sub s+1/-vs-s curves, we develop the natural extension of f/sub s/ to s< or =0. Explicit values for f/sub s/ and related quantities for ''almost random'' filling, k/sub 0/ = k/sub 1/, are obtained from a direct statistical analysis.

• Research Organization: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 50011
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 5539827
• 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
GROWTH
IRREVERSIBLE PROCESSES
KINETICS
NUCLEATION
ONE-DIMENSIONAL CALCULATIONS
PARTICLES
REACTION KINETICS
SOLID CLUSTERS