Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica-Effect of Pore-Level Anisotropy

The goal of this work is to understand adsorption-induced deformation of hierarchically structured porous silica exhibiting well-defined cylindrical mesopores. For this purpose, we performed an in situ dilatometry measurement on a calcined and sintered monolithic silica sample during the adsorption of N₂ at 77 K. To analyze the experimental data, we extended the adsorption stress model to account for the anisotropy of cylindrical mesopores, i.e., we explicitly derived the adsorption stress tensor components in the axial and radial direction of the pore. For quantitative predictions of stresses and strains, we applied the theoretical framework of Derjaguin, Broekhoff, and de Boer for adsorption in mesopores and two mechanical models of silica rods with axially aligned pore channels: an idealized cylindrical tube model, which can be described analytically, and an ordered hexagonal array of cylindrical mesopores, whose mechanical response to adsorption stress was evaluated by 3D finite element calculations. The adsorption-induced strains predicted by both mechanical models are in good quantitative agreement making the cylindrical tube the preferable model for adsorption-induced strains due to its simple analytical nature. The theoretical results are compared with the in situ dilatometry data on a hierarchically structured silica monolith composed by a network of mesoporous struts of MCM-41 type morphology. Analyzing the experimental adsorption and strain data with the proposed theoretical framework, we find the adsorption-induced deformation of the monolithic sample being reasonably described by a superposition of axial and radial strains calculated on the mesopore level. The structural and mechanical parameters obtained from the model are in good agreement with expectations from independent measurements and literature, respectively.