A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores

Abstract

We present a thermodynamic analysis of the mid-density scheme that was introduced recently as a simple alternative to more complex methods (such as the gauge cell and the thermodynamic integration procedures) for determining the equilibrium phase transition in pores. A construction of configurations having densities falling between those of the low- and high-density states inside the hysteresis loop is carried out with a canonical Monte Carlo simulation (NVT, where the number of particles N, the system volume V and the temperature T in the system are constant), and it is found that this ‘nucleation’ state has two coexisting phases of alternating liquid bridges and gas cavities. This state is maintained at a threshold chemical potential, μeq (obtained with the Widom insertion method), which is the coexistence chemical potential. When this ‘nucleation’ state is in contact with an infinite reservoir (grand canonical ensemble) of chemical potential less than μeq, the system will evolve to a low-density state. On the other hand, when it is exposed to a chemical potential greater than μeq, the system will evolve to a high-density state. We test this method with a number of examples of cylindrical pores, and investigate the effects of the pore size, the simulation box length for the case of infinite pores, the pore length for the case of finite pores and the temperature. When the pore is finite in length, the coexistence is no longer a first-order transition, like the one observed in an infinitely long pore, but instead shows a second-order transition with a continuous, but sharp change from a low-density state to a high-density state.