| 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 |