(733i) Statistical Thermodynamics of Two-Dimensional Fluids.

The growing interest in the description of the properties of fluids of restricted dimensionality has been followed by several attempts to implement an accurate and simple theoretical equation of state. In this work, we have developed an analytical perturbation-based equation of state (EoS) for the two-dimensional square-well model. This EoS is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1 ≤ d ≤ 3). The so-obtained EoS supports the implementation of a discrete perturbation theory able to account for general atomic potential shapes. The comparison between the theoretical and simulation results has been performed for the two-dimensional versions of the Lennard-Jones and Yukawa fluids. Then, we have naturally extended the theory to molecular fluids of both convex and dumbbell type by constructing effective intermolecular potentials with implicit shape dependence. The molecular EoS was tested against simulation results for the 2D-square-well, Kihara spherocylinder, and Lennard-Jones dumbbell models. We found that these theoretical approaches reproduced the EoS of the selected fluids quantitatively, but the vapor-liquid equilibrium was only grasped qualitatively. Reasons for this drawback are also discussed. Nevertheless, the theory presented here can be extended to molecular fluids under confinement, with configurational space of integer or non-integer dimension. This contribution is based on references [1,2].

References

[1] Víctor M. Trejos, Andrés Santos, Francisco Gámez. Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory. Journal of Chemical Physics, 148 194505(1)-194505(9), (2018).

[2] Francisco Gámez, Lucas F. Rodríguez-Almeida, Víctor M. Trejos. Thermodynamics of two-dimensional molecular fluids: Discrete perturbation theory and Monte Carlo simulations. Journal of Molecular Liquids, 300 112293(1)-112293(9) (2020).