Contact approximation kinetics

The theory of geminate recombination experienced a similar evolution from primitive exponential model and contact approximation [19,20], to distant recombination carried out by backward electron transfer [21], However, all these theories have an arbitrary parameter initial separation of reactants in a pair, / o. This uncertainty was eliminated by unified theory (UT) proposed in two articles published almost simultaneously [22,23], UT considers jointly the forward bimolecular electron transfer and subsequent geminate recombination of charged products carried out by backward electron or proton transfer. The forward transfer creates the initial condition for the backward one. This is the distribution of initial separations in the geminate ion pair/(ro), closely analyzed theoretically [24,25] and inspected experimentally [26,27], It was used to specify the geminate recombination kinetics accompanied by spin conversion and exciplex formation [28-31], These and other applications of UT have been covered in a review published in 2000 [32],... 

The geminate recombination is actually controlled by diffusion, if the initial separation of ions is so large that their transport from there to the contact takes more time than the reaction itself. The exponential model excludes such a situation from the very beginning, assuming that ions are bom in the same place where they recombine. Thus, EM confines itself to the kinetic limit only and fixes Z = z = const. The kinetic recombination in the contact approximation does not imply that the starts are taken from the very contact. If they are removed a bit and diffusion is fast, the recombination is also controlled by the reaction and its efficiency Z = qz is constant although smaller than in EM. 

According to the Smoluchowski theory of diffusion-controlled bimolecular reactions in solutions, this constant decreases with time from its kinetic value, k0 to a stationary (Markovian) value, which is kD under diffusional control. In the contact approximation it is given by Eq. (3.21), but for remote annihilation with the rate Wrr(r) its behavior is qualitatively the same as far as k(t) is defined by Eq. (3.34)... 

Dry, Kinetic Contact. Under kinetic conditions, the resistance measured at 30 V D.C. was even larger than that for a static contact. The resistance increased with the speed of sliding from a value of approximately 25 K at a speed of 10" cm/sec. to a value of over 100 K Q at a speed of 10 cm/sec. The large increase in resistance seems to occur at the transition from static to kinetic condition. 

Materials suitable for short-duration contact may not be suitable for longer service times. The kinetics of migration are, to a first approximation, first-order in that the extent of migration increases according to the square-root of the time of contact Moct1/2. The time (duration) of contact for common packaging can vary enormously and the performance requirements of the material must be specified accordingly ... 

In liquids the static kinetics precedes the diffusion accelerated quenching, which ends by stationary quenching. The rate of the latter k = AkRqD has a few general properties. In the fast diffusion (kinetic control) limit Rq — 0 while k —> ko. In the opposite diffusion control limit Rq essentially exceeds a and increases further with subsequent retardation of diffusion. As the major quenching in this limit occurs far from contact, the size of the molecules plays no role and can be set to zero. This is the popular point particle approximation (ct = 0), which simplifies the analytic investigation of diffusional quenching. For the dipole-dipole mechanism the result has been known for a very long time [70] ... 

However, at still larger concentrations only DET/UT is capable of reaching the kinetic limit of the Stem-Volmer constant and the static limit of the reaction product distribution. On the other hand, this theory is intended for only irreversible reactions and does not have the matrix form adapted for consideration of multistage reactions. The latter is also valid for competing theories based on the superposition approximation or nonequilibrium statistical mechanics. Moreover, most of them address only the contact reactions (either reversible or irreversible). These limitations strongly restrict their application to real transfer reactions, carried out by distant rates, depending on the reactant and solvent parameters. On the other hand, these theories can be applied to reactions in one- and two-dimensional spaces where binary approximation is impossible and encounter theories inapplicable. 

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