On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR

Nuclear magnetic resonance (NMR) diffusion measurements can be used to probe porous structures or biological tissues by means of the random motion of water molecules. The short-time expansion of the diffusion coefficient in powers of t1/2, where t is the diffusion time related to the duration of the diffusion-weighting magnetic field gradient profile, is universally connected to structural parameters of the boundaries restricting the diffusive motion. The t1/2-term is proportional to the surface to volume ratio. The t-term is related to permeability and curvature. The short time expansion can be measured with two approaches in NMR-based diffusion experiments: First, by the use of diffusion encodings of short total duration and, second, by application of oscillating gradients of long total duration. For oscillating gradients, the inverse of the oscillation frequency becomes the relevant time scale. The purpose of this manuscript is to show that the oscillating gradient approach is blind to the t-term. On the one hand, this prevents fitting of permeability and curvature measures from this term. On the other hand, the t-term does not bias the determination of the t1/2-term in experiments.