Diffusion-controlled reactions. II. Further bounds on the rate constant

Journal Article · Wed Feb 01 04:00:00 EST 1989 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.456655· OSTI ID:6549752

Torquato, S; Rubinstein, J

We apply variational principles derived earlier by us to obtain rigorous upper and lower bounds on the rate constant k associated with diffusion-controlled reactions among static, reactive traps. We derive a phase-interchanged interfacial-surface lower bound on k and a new type of lower bound which we term a ''void'' bound. Among other results, we compute the phase-interchanged interfacial-surface bound on k for a distribution of fully penetrable (i.e., randomly centered) spheres in which the trap region is the space exterior to the spheres (the ''holes'' between the spheres) and diffusion occurs in the sphere region. We also derive an upper bound on k for identical spherical traps (randomly or periodically arranged), and evaluate it for a simple cubic lattice.

• Research Organization: Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910
• OSTI ID: 6549752
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 90:3; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
CHEMICAL REACTION KINETICS
DIFFUSION
FLUID FLOW
FLUIDS
KINETICS
LIQUIDS
REACTION KINETICS
TRAPS
TWO-PHASE FLOW
VARIATIONAL METHODS