Abstract
Fluids confined in mesoporous solids exhibit a wide range of physical behavior including rich phase equilibria. While a notable progress in their understanding has been achieved for fluids in materials with geometrically ordered pore systems, mesoporous solids with complex pore geometries still remain a topic of active research. In this work we study phase transitions occurring in statistically disordered linear chains of pores with different pore sizes. By considering, quite generally, two phase change mechanisms, nucleation and phase growth, occurring simultaneously we obtain the boundary transitions and the scanning curves resulting upon reversing the sign of the evolution of the chemical potential at different points along the main transition branches. The results obtained are found to reproduces the key experimental observations, including the emergence of hysteresis and the scanning behavior. By deriving the serial pore model isotherm we suggest a robust framework for reliable structural analysis of disordered mesoporous solids.
Highlights
Better understanding of thermodynamics of mesoscopic systems, in particular of molecular systems confined to mesopore spaces, is important for very diverse fields including atmospheric and environmental sciences, food preservation, and nanotechnology
The independent domain theory developed by Everett for capillary phenomena[15], referred to here as the independent pore model (IPM), assumes that all pores with different pore sizes fill and empty independently from each other
Being useful for the exploration of some microscopic aspects accompanying the phase transitions, all these approaches cannot be implemented for the pore size analysis. It has been evident in the literature that already the simplest model representing random porous materials, namely a linear chain of pores with different pore sizes, in what follows referred to as the serial pore model (SPM), exhibits the key features observed in the experiments as exemplified by Fig. 1B33, 40, 41
Summary
Better understanding of thermodynamics of mesoscopic systems, in particular of molecular systems confined to mesopore spaces, is important for very diverse fields including atmospheric and environmental sciences, food preservation, and nanotechnology. It has been evident in the literature that already the simplest model representing random porous materials, namely a linear chain of pores with different pore sizes, in what follows referred to as the serial pore model (SPM), exhibits the key features observed in the experiments as exemplified by Fig. 1B33, 40, 41. The equations derived are generally applicable for predicting different phase equilibria, including gas-liquid and liquid-solid transitions The latter is validated using computer simulations of the respective models. This formalism is applicable for similar phenomena exhibiting pore-size dependent features These may include liquid-liquid separation and solid-solid transitions in confined space and mercury intrusion being the most representative examples. The final analytical results resemble the BJH scheme for the pore size analysis using IPM, but applied to SPM They provide a more accurate route for structural characterization of disordered porous materials
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