Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry

The time-dependent apparent diffusion coefficient as measured by pulsed gradient NMR can be used to estimate parameters of porous structures including the surface-to-volume ratio and the mean curvature of pores. In this work, the short-time diffusion limit and in particular the influence of the temporal profile of diffusion gradients on the expansion of the diffusion coefficient in powers of the diffusion time [1] is investigated. To this end, the correction coefficients in the expansion, which describe the effect of elongated gradient pulses, are computed using the double integral computation technique [2] [3] [4].

It is shown that flow-compensated waveforms, i.e. those whose first moment is zero, are blind to the term linear in diffusion time (t-term) since the respective correction coefficient vanishes. This term is proportional to mean curvature and surface permeability. On the one hand, this observation can be used to probe longer diffusion times with flow-compensated gradients, which may be beneficial when computing the surface-to-volume ratio from the sqrt(t)-term, because no corruption from the t-term occurs.

One the other hand, this observation of a vanishing coefficient of flow-compensated gradients may be exploited by designing "two-dimensional" experiments. To this end, a gradient waveform that smoothly interpolates between flow-compensated and bipolar waveform is proposed and the degree of flow-compensation is used as a second experimental dimension. This two-dimensional ansatz is shown to yield an improved precision when characterizing the confining domain. This technique is demonstrated in simulations and in experiments performed with cylindrical capillaries of 100 µm radius.