Mean pore diameters of 3D printed micro-capillaries using the matrix pencil method

The matrix pencil method (MPM) is an approach for quantitative analysis of the multi-exponential time-domain signals from relaxation and diffusion NMR experiments. In contrast to other signal processing methods, MPM relies on solving the generalized eigenvalue problem of a so-called matrix pencil, resulting in discrete values representing the different relaxation species. In this work, the methodology is extended from relaxation experiments towards assessment of NMR self-diffusion studies in micro-porous media on a length scale suitable for determining pore sizes from signal decays. For this, well-defined 3D nano printed micro-capillary structures are introduced as model porous media to correlate the apparent diffusion coefficients derived by MPM from pulsed gradient spin echo (PGSE) experiments to the pore diameter reported by the root-mean-square displacement (RMSD) of molecules diffusing in an array of many regular pores. Due to the high uniformity of the capillaries, the observed signal decay curves are modulated by diffusive diffraction. This phenomenon occurs when the paths of the diffusing spins are confined in an ensemble of identical pores, leading to repeated refocusing of phase coherence in q space. From the q values of the minima, the pore size can be determined for known pore shapes. This can be used as ground truth to validate the results from diffusometry experiments calculated by quantitative analysis methods such as MPM. Results show that MPM algorithm effectively quantifies the diameter within a restricted diffusion experiment. In addition, MPM separates two diffusion components and predicts the correct pore sizes as well as the respective relative contributions.