Kinetics of Reactant Isolation. I. One-Dimensional Problems

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Abstract
This paper treats the time‐dependent statistics of bond formation (both irreversible and reversible) between fixed sites. This model corresponds to a number of real physical processes. Among these are reaction of adjacent functional groups on a linear polymer, matrix isolation of free radicals, and chemisorption. Because the sites are fixed, certain of them become isolated from others, not yet reacted, and must survive to infinite time. A certain amount of survival occurs even when bonds can be undone. Exact descriptions of the kinetics of these processes are given for one‐dimensional systems. The mean probability of site survival as a function of time is calculated for linear arrays and for rings. The probability of site survival as a function of position on the chain (end effects) is treated in Sec. IV. A generating function is introduced in order to calculate higher moments of the survival probability distribution function and to treat the effect of a random diluent. An approximate method of solution is developed for the time dependence of the number of reacted particles in the reversible case.

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