Nuclear Magnetic Relaxation Spectroscopy

  • H. G. Hertz
Part of the Water book series (WCT)


As in all liquids, so, too, in water the molecules undergo thermal motion. The self-diffusion coefficient D describes the nature of the erratic translational motion:
$$\left\langle {{r^2}} \right\rangle {\mkern 1mu} = {\mkern 1mu} 6Dt$$
where 〈r2〉 is the mean square displacement of the water molecule after a time t. For water at 25°C, D = 2.31 × 10−5 cm2 sec−1,(580) so if we consider a mean square displacement of ∼a2, where a is the diameter of the water molecule, the time necessary for such a displacement is 6 × 10−12 sec. Equation (1) only holds if the time is long enough so that we actually have random motion, that is, the instantaneous velocity of the water molecule must have suffered a large number of changes in magnitude and direction. For times t ≳ 6 × 10−12 sec this condition is fulfilled.


Relaxation Rate Correlation Time Hydration Water Water Proton Rotational Correlation Time 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • H. G. Hertz
    • 1
  1. 1.Institut für Physikalische Chemie und ElektrochemieUniversität KarlsruheKarlsruheGermany

Personalised recommendations