Anisotropic Diffusion in Face-Centered Cubic Opals
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Abstract
Diffusion in face-centered cubic (fcc) opals synthesized from 250 nm-diameter silica spheres was investigated by electrochemical methods and finite-element simulations. Opal modified electrodes (OME) ((111) opal surface orientation) were prepared by thermal evaporation of Au onto ∼1 mm-thick opals. Linear sweep voltammetry of Au OMEs in aqueous solutions containing an electroactive molecule and a supporting electrolyte (0.1 M Na2SO4) was used to determine molecular diffusion coefficients, Dfcc, within the opal. Dfcc is related to the diffusion coefficient of the molecule in free solution, Dsol, by the relationship Dfcc, = (ε/τ)Dsol, where ε is the interstitial volume fraction of a fcc opal (ε = 0.260 for an infinitely thick opal) and τ is the tortuosity; the tortuosity reflects the increased distance traversed by molecules as they diffuse through the curved interstitial spaces of the opal lattice, and is a function of both the direction of transport relative to the lattice and the number of layers of spheres in the opal lattice. Finite-element simulations are used to compute τ for transport orthogonal to the (111), (110), and (100) surface orientations for 1−7 layers of spheres. Values of τ = 1.9 ± 0.7 and 3.1 ± 1.2 were obtained from experiment for transport of Ru(NH)63+ and Fe(CN)64- normal to the (111) surface, respectively, in reasonable agreement with a value of ∼3.0 obtained from the simulation.
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