Diffusion in Model Disordered Media

Abstract

We perform water self-diffusion measurements in ternary DDAB microemulsions near the structural transition point. This allows experimental investigation of the predicted anomalous diffusion behavior exhibited near a static percolation transition.Near the transition point time-dependent behavior is observed. The scaling behavior is consistent with theory for a static percolative medium. This is the first time anomalous diffusion has been experimentally measured in a well-characterized porous media.PACS numbers: 66.10.Cb, 05.70.Jk, 47.55.Mh, 64.60.Ak The prediction of effective transport properties of heterogeneous systems such as porous media is of considerable interest. In many cases, classical theories of transport, valid for homogeneous systems, do not apply if the heterogeneities are strong and broad enough. For example, transport and, in particular, diffusion in heterogeneous materials can be anomalous in the sense that classical laws of transport, such as Fick's law of diffusion with a constant diffusivity, are not valid, and instead one has a time-dependent transport coefficient. Much of our understanding of heterogeneous porous media and transport therein has been obtained by using percolation theory [1 -4]. Of particular interest is the behavior of transport properties near a percolation threshold p, . As p, is approached the correlation length s "diverges. The length scale s~m easures the macroscopic homogeneity of the system. For any length scale L ) se~the system is macroscopically homogeneous, and the classical equations of transport with constant transport coefficients are applicable. For length scales L~$~the system is heterogeneous, and the classical equations fail. For the classical Fick law of diffusion the mean square displacement of particles x2(t) is related to the effective (constant) diffusivity D, and time t as x (t) = D, t, where D, is a constant. For a heterogeneous system near its percolation threshold the diffusion law becomes anomalous [5 -7] and theory suggestsx'(t) = t', where 6 ( 1. Thus the diffusivity D, = x (t)/t is time dependent and vanishes as t~~. Two examples are a porous catalyst particle near its deactivation point (the point at which macroscopic diffusion in the pore space of the catalyst is no longer possible due to the plugging of the pores) and a porous medium that contains two immiscible phases, where one of the phases is disconnected. The slowing down of transport is associated with particles diffusing within dangling ends of percolation clusters.While a large body of theoretical work and simulations have predicted anomalous diffusion in percolative media [5,8 -12], no experimental system with a wellcharacterized microstructure has been available to test the prediction. Recently we showed that a class of ternary microemulsions provides such a system [13,14]. By tuning experimental variables one can realize a disordered "porous" medium with specific prescribed microstructures. This allows independent measurements of mechanical and transport properties.As volume fra...

Fluctuating Euler characteristics, topological disorder line, and passages in the lamellar phase

“…In real experiments the averaged configurations are obtained in small-angle neutron scattering experiments, whereas the snapshot configurations might be studied by freeze fracture microscopy or NMR. 32 We cannot however estimate on the basis of our research the time scale FIG. 5.…”

Simulation of small molecule diffusion using continuous space disordered networks

“…For anomalous diffusion to persist for a sufficiently long time to be observable experimentally, the jump network connectivity z must be sufficiently low such that it approaches the percolation threshold z c . For example, the experimental observation of anomalous diffusion in microemulsions was made under conditions known to correspond to a structural transition [22]. Even then, resolution at time scales below 100 ms is likely to be required.…”

“…Right at the percolation threshold, particles exhibit anomalous diffusion, with the exponent n depending on the connectivity exponent [20]. Such anomalous diffusion has also been observed experimentally [21][22][23].…”

A didodecyldimethylammonium bromide ternary system: Characterization of three‐phase stable emulsions by optical microscopy

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