Diffusion coefficient of proton

Value 7000 µm^2/sec
Organism Generic
Reference Noam Agmon, The Grotthuss mechanism, Chemical Physics Letters 244 (1995) 456-462, doi:10.1016/0009-2614(95)00905-J p.458 left column top paragraph
Method Using equation D=l^2/6τp, l as distance between hydronium ion and water, 0.25nm (BNID 106700) and tp as 1.5e-12sec (BNID 106698 comments section) (0.25µm×10^-3)^2/(6×1.5×10^-12sec)=6,944µm^2/sec ˜≈7,000µm^2/sec
Comments P.457 right column bottom paragraph: "(ii) The NMR proton hopping times, τp, account for the abnormal proton mobility if one assumes that hopping is across a single water molecule at a time. Using the Einstein relation for mobility in three dimensions D=l^2/6τp. Meiboom was able to estimate a reasonable proton diffusion coefficient [ref 26]. Let us slightly modify this estimate by taking the hopping length as l=2.5Å, the hydrogen-bond length between water and H30+ [ref 8], rather than the water-water distance of 2.8 Å. Using τp=1.5 ps gives D=7×10^-5 cm^2/s, a very reasonable estimate for the abnormal proton mobility at room temperature (subtract from the proton diffusion coefficient, 9.3×10^-5 cm^2/s, the water self-diffusion coefficient, 2.3×10^-5 cm^2/s [ref 1]). Even the most modest coherent effect, with proton hopping across just two water molecules, already leads to a factor of 4 in the predicted mobility. Thus proton mobility is best described as an incoherent, Markovian hopping process." Abnormal proton mobility at room temperature
Entered by Uri M
ID 106702