Abstract. A stochastic model of grain surface chemistry, based on a master equation description of the probability distributions of reactive species on grains, is developed. For an important range of conditions, rates of molecule formation are limited by low accretion rates, so that the probability that a grain contains more than one reactive atom or molecule is small. We derive simple approximate expressions for these circumstances, and explore their validity through comparison with numerical solutions of the master equation for H, O and H, N, O reaction systems. A more detailed analysis of the range of validity of several analytic approximations and numerical solutions, based on exact analytical results for a model in which H and H2 are the only species, is also made. Though the use of our simple approximate expressions is computationally efficient, the solution of the master equation under the assumption that no grain contains more than two particles of each species usually gives more accurate results in the parameter regimes where the deterministic rate equation approach is inappropriate. The implementation of sparse matrix inversion techniques makes the use of such a truncated master equation solution method feasible for considerably more complicated surface chemistries than the ones we have examined here.
This paper is concerned with the competition between recombination of a radical pair and radical attack on targets such as macromolecules or nanoparticles in solution, which are large on the molecular scale. The difference in scale between radicals and targets causes the kinetics to be transient over a long period. The specific novel feature of the analysis is the effect of the initial spatial correlation of the radicals on the kinetics of attack on the targets. The main results are (i) a simple modification of the Smoluchowski rate coefficient for scavenging and (ii) the probability of multiple hits on the same target. Both effects arise from the clustering of the radicals. The latter is of particular interest in radiation biology, because multiple hits result in complex damage. The analysis is validated against results from random flights computer simulation; excellent agreement is obtained.
An investigation into the kinetics of reaction between a diffusing particle and a system of two static spherical sinks is presented. The backward diffusion equation is solved for the probability of reaction with each sink, using both absorbing and radiation boundary conditions. The rate constants for each reaction are also calculated. The reactivity of the sinks is shown to be subadditive, and if the sinks are asymmetric the less reactive sink is more strongly affected by the competition. Competitive effects are found to be modeled adequately by using effective reaction radii. The IRT method is shown to have serious defects for such a system because of the correlation of the two sinks. An application to the reaction of OH radicals with thymidine is presented.
A theoretical investigation is presented of the competition between recombination of a geminate pair and reaction with an absorbing plane surface. Full random flights simulations are compared with the predictions of the independent pairs approximation for a variety of spatial configurations and, where possible, analytic solutions. Differences resulting from the competition are manifested as an underestimate of the amount of recombination and average hit-hit separation in the independent pairs relative to the random flights. These discrepancies are rationalized in terms of a correlation between the pair separation and the closest distance of the pair to the plane. The exact solution of a related one-dimensional problem is presented in order to give further insight into the correlation effect.
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