Effects of the Growth Kinetics on Solute Diffusion in Porous Films

Abstract

For the development of porous materials with improved transport properties, a key ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying solute diffusion through three-dimensional porous films produced by deposition models with controlled thickness and porosity. A competition between pore formation by lateral particle aggregation and surface relaxation that favors compaction is simulated by the lattice models of ballistic deposition and of random deposition with surface relaxation, respectively, with relative rates proportional to p and 1 − p. Effective diffusion coefficients are determined in steadystate simulations with a solute source at the basis and a drain at the top outer surface of the films. For a given film thickness, the increase in the relative rate of lateral aggregation leads to the increase in the effective porosity and the diffusivity, while the tortuosity decreases. Under constant growth conditions, the increase in the film thickness always leads to the increase in the effective porosity, but a nontrivial behavior of the diffusivity is observed. For deposition with p ≤ 0.7, in which the porosity is below 0.6, the diffusion coefficient is larger in thicker films; the decrease in the tortuosity with the thickness quantitatively confirms that the growth continuously improves the pore structure for diffusion. Microscopically, this result is associated with narrower distributions of the local solute current at higher points of the deposits. For deposition with p ≥ 0.9, in which the films are in the narrow porosity range ∼0.65−0.7, the tortuosity is between 1.3 and 2, increases with the thickness, and has maximal changes near 25%. Pairs of values of porosity and tortuosity obtained in some porous electrodes are close to the pairs obtained here in the thickest films, which suggests that our results may be applied to deposition of materials of technological interest. Noteworthy, the increase in the film thickness is generally favorable for diffusion in their pores, and the exceptions have small losses in tortuosity.

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