The rate coefficient for a partially reflecting boundary condition

4 THE RATE COEFFICIENT FOR A PARTIALLY REFLECTING BOUNDARY CONDITION 

To find the second-order rate coefficient for the reaction of A and B subject to the encounter pair reacting with a rate coefficient feact, the method developed in Sect. 3.7 can be used. Using eqn. (19), the rate coefficient, k(t), can be defined in terms of the diffusive current of B towards the central A reactant. But the partially reflecting boundary condition (22) equates this to the rate of reaction of encounter pairs. The observed rate coefficient is equal to the rate at which the species A and B could react were diffusion infinitely rapid, feact, times the probability that A and B are close enough together to react, p(R). 

this is a rather unwieldy expression. Since the arguments of the exponential and complementary error functions are generally large at experimentally accessible times, this expression can be simplifed to 

Thus the partially reflecting boundary condition reduces the effective encounter distance by a factor of fcact (4nRD + fcact) 1 for both the steady-state and transient terms in the rate coefficient. 

Obviously, the importance of diffusion on slow chemical reaction rates is small. It is only when the diffusion rate coefficient 4irRD is comparable with or less than the activation-limited rate coefficient that the effect of diffuse process becomes apparent. Noyes [5] pointed out that the steady-state rate coefficient of eqn. (26) is k(°°) and this can be written as 

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