Derjaguin-Broekhoff-de Boer analysis of adsorption in very disordered mesopores using probabilistic models

Our current ability to produce mesoporous materials with ordered morphology has raised fascinating questions about the impact of geometrical disorder on adsorption and desorption states [1]. Many recent works have investigated the role of mild elements of disorder, such as local constriction or corrugation superimposed to otherwise geometrically ideal cylindrical pores [2,3]. These works have notably shown that elements of disorder may act as nucleation sites and destabilize vapor-like metastable states. The relevance of these perturbation-like results to fundamentally disordered materials, such as gels, is unclear. In particular, do vapor-like metastable states exist at all in this type of very disordered material?

In the present communication, we address this question using probabilistic models to investigate the role of disorder. We generalize the classical Gaussian field models of porous materials [4] and use them to analyze adsorption and desorption in the Derjaguin-Broekhof-de Boer approximation. Our approach differs from earlier contributions in that both the adsorbent and the adsorbate are described in terms of probabilities [5]. This enables us to analyze the adsorbate configuration in very disordered solids using a low-dimensional yet realistic configuration space. We notably show that vapor-like metastable states are unlikely in gel-like disordered materials.