Theoretical Treatment of the Kinetics of Diffusion-Limited Reactions Export

@article{citeulike:1538999, abstract = {The problem of the kinetics of the diffusion-limited reaction A + B → AB has been formulated in terms of the pair probability densities of the reacting particles (every A taken with every B ). The alteration of these pair densities due to diffusion and reaction have been considered. The competition of every A for every B and the removal of particles from the system upon reaction have been appropriately accounted for. The formulation leads to a set of coupled differential equations that can be solved for a variety of boundary conditions. The problem has been solved in detail for a random initial distribution. The rate of reaction at any time is just the probable rate at which a single A and a single B diffuse together (with an appropriate boundary condition for reaction on close approach) multiplied by the product of the number of A 's and the number of B 's present at that particular time. The rate of the reaction A + B → AB will be second order and the reaction A + B → B will be first order after times long compared to a transient whose form is given explicitly. More general equations are obtained to permit the treatment of non-random initial distributions; as occur; for example; in the annealing of radiation damage. In such cases the irregular transients may account for a major portion of the reaction.}, author = {Waite, T. R.}, citeulike-article-id = {1538999}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.107.463}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v107/i2/p463_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v107/i2/p463_1}, day = {15}, doi = {10.1103/PhysRev.107.463}, journal = {Physical Review Online Archive (Prola)}, keywords = {diffusion-limited, journalclub, kinetics, reactions, smoluchowski, theory}, month = {Jul}, number = {2}, pages = {463--470}, posted-at = {2009-10-19 21:37:53}, priority = {5}, publisher = {American Physical Society}, title = {Theoretical Treatment of the Kinetics of Diffusion-Limited Reactions}, url = {http://dx.doi.org/10.1103/PhysRev.107.463}, volume = {107}, year = {1957} }

TY - JOUR ID - citeulike:1538999 L3 - citeulike-article-id:1538999 N2 - The problem of the kinetics of the diffusion-limited reaction A + B → AB has been formulated in terms of the pair probability densities of the reacting particles (every A taken with every B ). The alteration of these pair densities due to diffusion and reaction have been considered. The competition of every A for every B and the removal of particles from the system upon reaction have been appropriately accounted for. The formulation leads to a set of coupled differential equations that can be solved for a variety of boundary conditions. The problem has been solved in detail for a random initial distribution. The rate of reaction at any time is just the probable rate at which a single A and a single B diffuse together (with an appropriate boundary condition for reaction on close approach) multiplied by the product of the number of A 's and the number of B 's present at that particular time. The rate of the reaction A + B → AB will be second order and the reaction A + B → B will be first order after times long compared to a transient whose form is given explicitly. More general equations are obtained to permit the treatment of non-random initial distributions; as occur; for example; in the annealing of radiation damage. In such cases the irregular transients may account for a major portion of the reaction. IS - 2 JF - Physical Review Online Archive (Prola) EP - 470 TI - Theoretical Treatment of the Kinetics of Diffusion-Limited Reactions PB - American Physical Society VL - 107 SP - 463 KW - diffusion-limited KW - journalclub KW - kinetics KW - reactions KW - smoluchowski KW - theory AU - Waite, TR PY - 1957/Jul/15/ UR - http://dx.doi.org/10.1103/PhysRev.107.463 ER -