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A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

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Abstract

This work numerically investigates the diffusion of finite inert tracer particles in different types of fixed gels. The mean square displacement (MSD) of the tracers reveals a transition to subdiffusive motion MSD ∼ tα as soon as the accessible volume fraction p in the gel decreases from unity. Individual tracer dynamics reveals two types of particles in the gels: mobile tracers cross the system through percolating pores following subdiffusive dynamics MSDmobtαmob, while a fraction ptrap(p) of the particles remain trapped in finite pores. Below the void percolation threshold p < pc all the particles get trapped and α → 0. By separately studying both populations we find a simple phenomenological law for the mobile tracers αmob(p) ≈ a ln p + c where c ≈ 1 and a ∼ 0.2 depends on the gel type. On the other hand, a cluster-analysis of the gel accessible volume reveals a power law for the trapping probability ptrap ∼ (p/pc)γ, with γ ≃ 2.9. This yields a prediction for the ensemble averaged subdiffusion exponent α = αmob(1 − ptrap). Our predictions are successfully validated against the different gels studied here and against numerical and experimental results in the literature (silica gels, polyacrylamide gels, flexible F-actin networks and in different random obstacles). Notably, the parameter a ∼ 0.2 presents small differences amongst all these cases, indicating the robustness of the proposed relation.

Graphical abstract: A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

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Publication details

The article was received on 25 Sep 2018, accepted on 13 Nov 2018 and first published on 14 Nov 2018


Article type: Paper
DOI: 10.1039/C8SM01961D
Citation: Soft Matter, 2018, Advance Article
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    A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

    N. Alcázar-Cano and R. Delgado-Buscalioni, Soft Matter, 2018, Advance Article , DOI: 10.1039/C8SM01961D

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