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1SCIentIFIC REPORtS | 7: 7216 | DOI:10.1038/s41598-017-07406-2
Phase transitions in disordered mesoporous solids Daniel Schneider, Daria Kondrashova & Rustem Valiullin
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.
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. Due to a beneficial combination of high specific surface area and favorable transport properties mesoporous solids are currently considered as attractive host materials for use in practi- cal applications such as catalysis, sensing, and medicine. Hence, a thorough understanding of fluid behavior in mesopore spaces is an important basis for their technological usage and for improvement of structure charac- terization methods for mesoporous solids. Notably, the most widely used characterization approaches, such as gas sorption and thermoporometry, are based on the measurements of the pore size-dependent alterations of the phase transition points of confined matter1, 2. In the recent decades, significant progress in the understanding of the confinement effects was facilitated by the emergence of mesoporous solids with ordered porosities3–5. The experimental results obtained with these materials and advancements of theoretical approaches majorly contrib- uted to improve our knowledge about the microscopic processes occurring in porous materials with simple pore structures2, 6–13. At the same time, phase transitions in porous solids with complex pore architectures still remain poorly understood.
It is well recognized that phase transitions in materials with ordered and disordered pore systems differ sub- stantially. As an example, Fig. 1 shows schematically gas sorption isotherms typically obtained at sub-critical temperatures for porous solids with cylindrical pore geometries, like MCM-41 or SBA-1514, and with ran- dom materials, like Vycor porous glass15, 16. Similar patterns are also reported for melting and freezing in con- fined spaces17–22. In both cases shown in Fig. 1A,B there is irreversibility between the capillary-condensation (gas-liquid) and evaporation (liquid-gas) transitions. However, the shapes of the hysteresis loops are found to be substantially different. Thus, in cylindrical pores the two transition branches are parallel to each other and the irreversibility is known to be caused by metastability along the adsorption branch. The two transition branches will also remain to be parallel to each other for a collection of independent channels with different pore diameters, but they will appear not as steep as for one single channel. In contrast, the hysteresis loop in disordered materials is often found to be asymmetric with both transitions being dominated by complex free-energy landscape23, 24. Even stronger divergences are found for the scanning curves, i.e. curves obtained by reversing the sign of the evolution of the gas pressure at different points along the main transition branches. In the former case (uniform pores) the adsorption and desorption scans cross between the boundary curves25, while in the latter case (dis- ordered pores) the scanning curves merge at either the hysteresis upper or lower closure points. Interestingly and somewhat intriguingly, the patterns expected for disordered solids have also been observed with ordered MCM-41 and SBA-15 materials26, 27. Similarly, disordered porous solids may also exhibit the transition patterns resembling that of ideal materials28.
Felix Bloch Institute for Solid State Physics, University of Leipzig, Leipzig, Germany. Correspondence and requests for materials should be addressed to R.V. (email: email@example.com)
Received: 9 February 2017
Accepted: 23 June 2017
Published: xx xx xxxx