Can Electroactive Tracer Molecules Reveal Viscoelastic Structure by Measuring Non-Fickian Diffusion?

We find that viscous and viscoelastic fluids are distinguishable by gauging Non-Fickian diffusion of dissolved electroactive molecules. Typically, such fluids are differentiated by measuring the mean-squared-displacement <Δr²> of embedded tracer particles (~1 μm) diffusing over time (t). From the relationship <Δr²>=6Dt^α (D=particle diffusivity), log plots of <Δr²>vs.t^α reveal regimes encoded in the slope α. For Fickian diffusion α=1, whereas α<1 and α>1, indicate Non-Fickian sub- and super-diffusion, respectively. Here, we electrolyzed redox reporters as molecular tracers in selected fluids. The current (I) relationship I $$ v^1/2 (v=scan-rate) was recast as I²vs.1/t^α to introduce α as Non-Fickian quantifier in log plots. When viscosity increased at high concentration of small-molecules, D for the redox reporter declined but α remained constant at ~1 (Fickian). In contrast, both D and α(<1) decreased in viscoelastic hydrogels confirming a molecular sub-diffusive regime. These results agree with particle microrheology on the same fluid types using optical methods that are inapplicable to molecules. By quantifying Non-Fickian diffusion of electroactive molecular tracers, our method can uncover diffusion-structure relationships to identify regulators in neurodegenerative liquid-solid transitions of protein aggregates. Unlike tracer particles, the diffusivity of tracer molecules is controlled by the applied potential and electrode size.