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arXiv · 2604.13929

Three-dimensional photon transport in spinodal photocatalytic aerogels: how bicontinuous morphology controls kinetic rate constants

Renaud A. L. Vallée
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Abstract

Anatase TiO2 dispersed in a silica aerogel matrix forms porous monolithic photocatalysts promising for indoor air purification and VOC photo-degradation. Their bicontinuous spinodal architecture provides high surface area, structural integrity, and intense UV multiple scattering. Extracting kinetic descriptors from apparent rate constants requires an optical model for the photon fluence, and current practice replaces the 3D pore network by a homogeneous 1D slab with effective optical coefficients -- an approximation never quantified for spinodal geometries. We combine realistic 3D spinodal pore masks from Cahn-Hilliard spectral integration with 3D GPU-accelerated Monte Carlo (MC) photon-migration simulations, introducing the solid-phase-weighted estimator $\Phi_{3D}$ and comparing it with the conventional volume average $\Phi_{1D}$ and the diffusion-approximation (DA) prediction $\Phi_{DA}$. The ratio $\Phi_{3D}/\Phi_{1D}$ equals 1.515 at porosity $\phi=0.70$ and 1.774 at $\phi=0.90$: the solid phase is preferentially illuminated, traced to optical phase contrast. Since pores neither absorb nor scatter, photons cross quasi-ballistically, and the void phase sustains only $r=0.514$ of the solid-phase fluence, diluting the volume average with dark voxels. This ratio is porosity-independent, so the concentration ratio obeys the exact relation $1/[\phi r+(1-\phi)]$, reproducing both simulated values. The kinetic descriptor $k_{surf}\cdot K_{ads}$ is underestimated by 20% via the DA route and overestimated by 51.5% via the volume-averaged route. Homogeneous-slab MC simulations at matched optical thickness show that 84% of the fluence-weighted RMS discrepancy between MC and DA is intrinsic to the bicontinuous architecture and beyond any effective-medium DA. These results give a quantitative correction for kinetic extraction and design rules linking porosity, pore size and photon utilisation.

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Renaud A. L. Vallée. 2026-04-15. Three-dimensional photon transport in spinodal photocatalytic aerogels: how bicontinuous morphology controls kinetic rate constants. https://arxiv.org/abs/2604.13929

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