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Monte Carlo simulations in the grand ensemble and meso-canonical ensemble in which the adsorbent is connected to a finite reservoir have been used to study adsorption isotherms for monolayer argon adsorption on graphite at temperatures below the 2D-critical temperature in order to elucidate the microscopic details of the 2D-transitions: vapour–solid, vapour–liquid and liquid–solid. An S-shaped van der Waals (vdW) loop was found when a small square surface was used; however, for large square surfaces and rectangular surfaces the isotherms exhibit a vdW-type loop with a vertical segment which indicates the coexistence of two phases separated by a boundary that changes its shape with the loading. This coexistence occurs at the same chemical potential as determined by the mid-density scheme, developed by Do and co-workers (Z. Liu, L. Herrera, V.T. Nguyen, D.D. Do, and D. Nicholson, A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 37(11):932–939, 2011; Z. Liu, D.D. Do, and D. Nicholson, A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 38(3):189–199, 2011). [ABSTRACT FROM PUBLISHER]

In this paper, we report a comprehensive analysis of the adsorption of argon in cylindrical pores of finite length having different dimensions and adsorbent energies. We determine the mechanisms of adsorption and desorption in the hysteresis region, and use the recently introduced mid-density scheme, as an approximate method, to determine the equilibrium transition, which is found to lie wholly within the loop and closer to the desorption branch. For a given loading in the hysteresis region, we determine the microscopic behaviour of two metastable states (one on the adsorption branch and the other on the desorption branch) and the stable equilibrium state. The adsorption metastable state is characterised by a bulging adsorbed layer, while the desorption metastable state is characterised by a liquid bridge with a meniscus at each end in the shape of a long elliptical cone. The equilibrium state has a configuration that displays a liquid bridge with hemispherically shaped menisci having areas less than those of the two menisci in the desorption metastable state. [ABSTRACT FROM AUTHOR]

The recently proposed mid-density scheme [Liu Z, Herrera L, Nguyen VT, Do DD, Nicholson D. A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 2011; 37(11):932–939, Liu Z, Do DD, Nicholson D. A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 2012; 38(3):189–199] is tested against a method 2V-NVT (similar to the well-established gauge cell method) and the canonical ensemble (CE) method, using argon adsorption at 87 K in graphitic slit pores of infinite and finite length. In infinitely long pores, the equilibrium transition is vertical that is expected for an infinite system to have a first-order transition and this vertical transition was found to lie at the middle of the hysteresis loop and satisfies the well-known Maxwell rule of equal area. For pores of finite length, the equilibrium transitions are steep and are close to, but not exactly identical to, the desorption branch. This lends support to the conventional view that the desorption branch is nearest to equilibrium, although both adsorption and desorption branches are strictly speaking metastable; a view proposed originally by Everett [Everett DH. Capillary condensation and adsorption hysteresis. Berichte Der Bunsen-Gesellschaft [Phys Chem Chem Phys]. 1975; 79(9):732–734]. As a consequence, the Maxwell rule of equal area does not apply to finite systems. As the widely accepted CE and gauge cell methods do not falsify the mid-density scheme, this study lends strong support to the validity of this technique for the study of equilibria. [ABSTRACT FROM PUBLISHER]

A new and simple method to determine equilibrium phase transition in adsorption systems exhibiting a hysteresis loop is presented as an alternative to methods such as multiple histogram reweighting, gauge cell method and thermodynamic integration. This method is based on the NVT-grand canonical Monte Carlo mid-density scheme to determine the coexistence chemical potential and coexistence densities of an adsorption system. We illustrate this new scheme with argon and methane adsorption in a number of model solids having slit and cylindrical pores. This method does not have a strong basis on thermodynamic ground, but it does provide a simple heuristic approach that is simpler to understand physically. [ABSTRACT FROM AUTHOR]