Simulation-based characterization of electrolytes and small molecule diffusion in oriented mesoporous silica thin films

Mesoporous silica films offer exciting potential for the delivery of molecular cargo, detection of molecular agents and as environment-dependent ‘nanoreactors’ in biological systems. Fundamentally important to realizing this potential are quantitative models for how material topology, surface chemistry and surface/solution interfaces govern molecular transport (via diffusion). Partial differential equation (PDE)-based approaches are particularly well suited for reaction–diffusion processes in materials, given the ability to incorporate into the important simulation details including material morphology, surface chemistry and charge. However, two challenges that hinder the application of reaction–diffusion partial differential equations (PDEs) to structurally realistic models of materials are (1) burdensome post-processing and annotation of microscopy data needed for PDE solutions and (2) challenges in extrapolating model predictions determined at the nanoscale to heterogeneous materials. To address this gap, we developed a new workflow for simulating ion reaction–adsorption–diffusion in nanoporous silica-based materials that are resolved through electron microscopy. Firstly, we propose a matched filtering procedure to identify and segment unique porous regions of the material that will be subject to PDE simulation. Secondly, we perform reaction–adsorption–diffusion PDE simulations on representative material regions that are then applied to characterize the entire microscopy-resolved film surface. Using this model, we examine the capacity of a recently synthesized mesoporous film to tune small molecule permeation through modulating the material permeability, surface chemistry including buffering and adsorption, as well as electrolyte composition. Specifically, we find that our proposed matched filtering approach reliably discriminates hexagonal close-packed (HCP) porous regions (bulk) from characterized defect regions in transmission electron microscopy data for nanoporous silica films. Further, based on our implementation of a pH-/surface-chemistry-dependent Poisson–Nernst–Planck (PNP) model that is consistent with existing experimental measurements of KCl and CaCl₂ conductance, we characterize ion and 5(6)-Carboxyfluorescein (CF) dye permeability in silica-based nanoporous materials over a broad range of ionic strengths, pHs and surface chemistries. Using this protocol, we probe conditions for selectively tuning small molecule permeability based on mesoporous film pore size, surface charge, ionic strength and surface reactions in the rapid equilibrium limit. Altogether, this framework provides means to utilize and validate high-resolution microscopy data of mesoporous materials, from which spatially heterogeneous transport parameters can be estimated. As such, the protocol will have significance for characterization of new materials for wide-ranging applications.