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Reconciliation of different simulation methods in the determination of the equilibrium branch for adsorption in pores

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.