Separation of Bulk, Surface, and Topological Contributions to the Conductivity of Suspensions of Porous Particles

Abstract

Electromigration of ions through porous silica particles dispersed in an electrolyte is studied by conductivity measurements. By determining the suspension conductivity at infinite dilution of particles where the Maxwell equation is applicable, the conductivity of the particles is determined. At high ionic strength, this allows calculation of the tortuosity of the particles. The tortuosity is then used to extract the pore conductivity from the particle conductivity under low ionic strength conditions where the surface conductivity is not negligible. Evolution of pore conductivity, which appears to be related to pore size, is not monotonous when ionic strength increases, showing first a decrease at very low ionic strengths, i.e., in conditions of double layers overlap in the pores, followed by an increase to trend toward the bulk conductivity at high ionic strength. This unexpected behavior can be explained by the fact that the initial surface conductivity in pores is mainly due to the protons, provided by spontaneous dissociation of surface silanol sites in water, which are subsequently exchanged by sodium.

Dense inorganic electrolyte particles as a lever to promote composite electrolyte conductivity

“…This set of equations has been verified experimentally in the case of aqueous dispersion of dense silica spheres 41,44 . Basically, the inverse of tortuosity can be understood as an efficiency factor of the porous structure, with sinuous paths and dead ends, versus the ionic flux.…”

“…Indeed, the extent of the length of the double layer (space charge layer on the side of the liquid electrolyte, stabilizing the liquid electrolyte/ceramic interface) increases when the salt concentration decreases, leading to a higher charge concentration in a significantly large volume at the surface of the ceramic particles. 44,47 This may cause a localized conductivity that is far higher than that of the bulk electrolyte, so the ceramic particles appear to be more conductive. Conversely, at high salt concentrations, the double layer will concern such a small volume that surface effects will be negligible.…”

Multiscale adsorption and transport in hierarchical porous materials

“…[138][139][140] Despite its usefulness, there are only limited ways to predict the tortuosity of a given porous medium (except from numerical simulations such as random walk simulations mentioned above). In the case of the transport of electrolyte solutions, Denoyel and coworkers [141][142][143] have shown that the conductivity of suspensions of porous spherical particles can be predicted from the bulk conductivity and the particle conductivity using the Maxwell equation. 144 As far as hierarchical porous materials are concerned, while the benefits of combining porosities have been demonstrated (ref.…”

Impact of surface diffusion on transport through porous materials

“…Models such as the effective medium theory (EMT), including the Maxwell model [14], are often used to separate both contributions and to determine the particle diffusion coefficient 𝐷 𝑝𝑧 corresponding to the porous zones. The Maxwell model can also be used to determine the particle tortuosity by means of electrical measurements [15,16]. Higher order models such as Torquato model [17] can also be used but in this model the so-called three-point parameter 2 is unknown.…”

“…The particle tortuosity can also be calculated using the following equation: p = 1p ln 𝜀 𝑝𝑧 in which p is a topological parameter and 𝜀 𝑝𝑧 the particle porosity. This equation can be established theoretically for freely overlapping spheres (Weissberg equation) [20] and generalized to other systems using p as a free parameter [15,16,21,22,23,24,25]. The p values obtained by means of the peak parking method are around 1.4 for silica columns.…”