Spatio-temporal anomalous diffusion in heterogeneous media by NMR

TL;DR

This paper experimentally investigates anomalous diffusion in confined colloidal systems using NMR, confirming CTRW model predictions by measuring fractional exponents related to disorder and particle properties.

Contribution

First experimental measurement of the diffusion phase diagram in confined systems, validating CTRW predictions through simultaneous measurement of fractional exponents.

Findings

The temporal exponent $oldsymbol{lpha}$ depends on system disorder.

The spatial exponent $oldsymbol{mu}$ depends on bead size and magnetic susceptibility.

Results fully match CTRW theoretical predictions.

Abstract

For the first time, the diffusion phase diagram in highly confined colloidal systems, predicted by Continuous Time Random Walk (CTRW), is experimentally obtained. Temporal and spatial fractional exponents, $\alpha$ and $\mu$, introduced within the framework of CTRW, are simultaneously measured by Pulse Field Gradient Nuclear Magnetic Resonance technique in samples of micro-beads dispersed in water. We find that $\alpha$ depends on the disorder degree of the system. Conversely, $\mu$ depends on both bead sizes and magnetic susceptibility differences within samples. Our findings fully match the CTRW predictions.