Small Molecules short timescales

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

There are a number of points of view one can take in trying to understand physical or chemical processes. A full microscopic picture involves the motion of individual atoms and molecules, or even electrons and nuclei. For small systems this is a feasible approach, for instance for molecular collisions in vacuum, or for processes occurring in a small part of a much larger system on a very short timescale such as the first proton transfer steps in a photoactive protein following excitation by a fast laser pulse. But for a moderately large system, it is problematic. Accuracy of quantum calculations for tautomeric equiUbrium constants is a few kilocalories per mole, which does not even allow a reasonable prediction of equilibrium constants in vacuum, let alone in solvents. Prediction of rate constants is out of the question. 

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