Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers

Abstract

The application of pulsed gradient spin echo nuclear magnetic resonance (NMR) to the case of molecules trapped between two plane parallel boundaries, has been examined theoretically, with computer simulation and by experiment. A new closed-form analytic expression is obtained for the averaged propagator and the echo attenuation when the walls have finite relaxivity and this expression is verified by computer simulations. It is shown that ‘‘diffraction’’ effects are still strongly apparent when wall relaxation is taken into account and that deviations in the barrier spacing parameter obtained from the position of the echo minimum, are weak. In particular we show that for the pulsed gradient spin echo (PGSE) pulse separation time on the order of a2/2D, the deviation is less than 10% provided that the relaxation is not so severe as to reduce the zero gradient signal amplitude below 10% of its unrelaxed value. We further examine the influence of finite gradient pulse and find, as with wall relaxation, that diffusion during the gradient pulse has the effect of shifting to higher q the position of the first minimum in the echo diffraction pattern. The diffusive diffraction effect is demonstrated experimentally using a stack of pentane-filled microcapillaries of wall spacing 100 μm, and fits to the data yield realistic values for the known experimental parameters.