A single-shot measurement of time-dependent diffusion over sub-millisecond timescales using static field gradient NMR

Abstract

Time-dependent diffusion behavior is probed over sub-millisecond timescales in a single shot using an NMR static gradient, time-incremented echo train acquisition (SG-TIETA) framework. The method extends the Carr-Purcell-Meiboom-Gill (CPMG) cycle under a static field gradient by discretely incrementing the $π$-pulse spacings to simultaneously avoid off-resonance effects and probe a range of timescales ($50 - 500$ microseconds). Pulse spacings are optimized based on a derived ruleset. The remaining effects of pulse inaccuracy are examined and found to be consistent across pure liquids of different diffusivities: water, decane, and octanol-1. A pulse accuracy correction is developed. Instantaneous diffusivity, $D_{\mathrm{inst}}(t)$, curves (i.e., half of the time derivative of the mean-squared displacement in the gradient direction), are recovered from pulse accuracy-corrected SG-TIETA decays using a model-free, log-linear least squares inversion method validated by Monte Carlo simulations. A signal-averaged, 1-minute experiment is described. A flat $D_{\mathrm{inst}}(t)$ is measured on pure dodecamethylcyclohexasiloxane whereas decreasing $D_{\mathrm{inst}}(t)$ are measured on yeast suspensions, consistent with the expected short-time $D_{\mathrm{inst}}(t)$ behavior for confining microstructural barriers on the order of microns.