Theory of electron-nucleus Overhauser effects in liquids containing free radicals

Abstract

The nuclear magnetic relaxation and the electron-nucleus Overhauser effect on spin ½ nuclei in solutions containing free radicals are calculated on the assumption that the nuclei and electrons interact by means of magnetic dipole–dipole interactions and scalar spin–spin interactions. The time dependence of the dipole–dipole interactions is assumed to be due to the translational diffusion of the free radicals and the molecules containing the nuclei. Two models are employed for the scalar interactions. In the first of these, there is a scalar interaction only while a molecule is stuck to a free radical, and the time for which they are stuck is a random variable. In the second model, the hypothesis is made that the scalar interaction is a very short range interaction with magnitude ħA ( d/R ) exp [– λ ( R–d )], where λ d ≫ 1, A and λ are constants, R is the distance between a nucleus and an electron, and d is a distance of closest approach, inside of which the interaction is zero. In the second model, the time dependence of the scalar interaction, as in the case of the dipole–dipole interactions, is due to the relative diffusion of the molecules and free radicals in the solution. For the second model, it is found that the frequency dependence of the spectral density of a scalar interaction is very similar to the frequency dependence of the spectral density of a dipole–dipole interaction, no matter how short range the scalar interaction is made by making λd very large. For both models of the scalar interaction it is found that the sign of the steady-state Overhauser effect may change from positive to negative as the magnetic field is increased, but that this is more likely to happen for the first model of the scalar interactions than for the second. The interpretation of experiments in terms of the results derived here is discussed, with particular attention given to experiments performed at two different magnetic fields. It is found that in some cases it may be possible to determine which model of the scalar interactions gives better agreement with experiment, and to determine values for the contributions of the scalar and the dipolar interactions, the distance of closest approach, and the relative diffusion coefficient.