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Mathematical Physics Seminar

In-Person: Alexander Neimark - Mesocanonical Ensemble to Study Equilibrium and Hysteretic Transitions in Confined Nanophases

Location:  Hill 705
Date & time: Thursday, 25 April 2024 at 12:10PM - 1:10PM


Alexander Neimark - Rutgers University


April 25th, 12:10pm; Hill Center 705

Mesocanonical Ensemble to Study Equilibrium and Hysteretic Transitions in Confined Nanophases

Phase transitions in fluids confined by nanoscale constraints are affected by geometric restrictions and guest-host interactions. Nanophase transitions, which demonstrate characteristic signatures of 1st order phase transitions, often involve long-lasting metastable states and hysteresis that is well-documented in gas adsorption-desorption experiments with various nanoporous materials. From the positions of statistical mechanics, a rigorous interpretation of these observations represents a fundamental problem. Nanoscale systems are essentially small, finite volume systems, in which the thermodynamic functions are analytical so that the very definition of phase transitions should be revisited. The concept of the thermodynamic limit is no longer valid, and the statistical ensembles (canonical and grand canonical) are not equivalent. The mesoscopic canonical, or mesocanonical, ensemble (MCE) is devised to study the nanophase behavior under conditions of controlled fluctuations that allows to stabilize metastable and labile states. In the MCE, the system of interest (fluid confined a nanopore, or a system of nanopores) is considered in equilibrium with a reservoir of limited volume, called the gauge cell, which controls the allowable level of density fluctuations.  In this respect, the MCE is a middle ground between the grand canonical ensemble, which permits unlimited density fluctuations, and the canonical ensemble, which considers a close system. The MCE Monte Carlo simulations produce van der Waals type isotherms with distinctive swings around the phase transitions regions.  The constructed isotherms determine the positions of phase equilibrium, spinodals, and nucleation barriers for observed phase transitions. Advantages of the MCE method is demonstrated on various examples of adsorption and capillary condensation on nanoporous systems, focusing on quantitative description of available experimental data.

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