Partial structural order of gel-forming material detected as multimodal subdiffusion by logarithmic measure

Fibrous nanomaterials suspended in liquid form gel structures when the binding sites between the components reach sufficient number densities. Cellulose nanofibers (CNFs) are one of such nanomaterials, and transparent papers are fabricated by drying their aqueous dispersions. It is therefore important to characterize the wet state, but the specific fluorescent marker molecules are not available for arbitrary CNFs. We report an approach based on the single particle tracking of Brownian probe particles. We focus on the nonuniformity in the Brownian motion to detect the partial structural order between sol and gel, which is nontrivial to characterize. The simple logarithmic measure of diffusive behavior reveals the multimodal nature of Brownian motion depending on the CNF concentration. The subdiffusive behavior by the overall mean squared displacements alone does not tell whether it is caused by confinement in the local environment by CNFs, or binding to single CNFs possibly diffusing in the dispersion. However, the particle-size dependence clarifies that it is not caused by binding but the confinement effect. Furthermore, the logarithmic measure approach enables the detection of overlapping distributions through their heads rather than tails. The detection of partial structural order by rheological non-uniformity of the system with a simple approach will contribute to the further understanding of gel forming materials in general.