Low temperature behavior of thermodynamic perturbation theory

Monte Carlo simulations have been carried out for a hard sphere square well model fluid with well widths of lambda = 1.01, 1.02 and 1.04 to obtain thermodynamic properties, such as pressure, excess Helmholtz free energy and internal energy, constant volume excess heat capacity, excess chemical potential, and excess enthalpy. The extremely narrow well widths considered allowed us to perform simulations at extremely low temperatures without reaching the liquid-vapour transition, which is metastable for these values of lambda. These simulation data have been used to explore the low temperature behavior of two thermodynamic perturbation theories (TPT), namely a high temperature series expansion truncated at second order within the local compressibility approximation (thereafter denoted as 2nd-order LCA-TPT) and a recently proposed coupling parameter series expansion truncated at 3rd-, 4th- and 5th-order (thereafter denoted as 3rd-order, 4th-order and 5th-order TPT, respectively). It has been found that the 2nd-order LCA-TPT is qualitatively incorrect in most of the cases analyzed, whereas the 3rd-order TPT is quantitatively correct in most of them. With increasing the well width, and consequently the temperatures considered, the 3rd-order TPT quickly becomes more accurate. Among the six thermodynamic quantities analyzed, the one most difficult to predict accurately is the constant volume excess heat capacity, for which the TPT based on the coupling parameter expansion provides satisfactory results only in the case of lambda = 1.04. For the cases studied, the performance of the 3rd-order, 4th-order, and 5th-order TPT are essentially equal; the change of the order of the truncation sometimes results in an improvement of some thermodynamic quantities within certain regions of the thermodynamic surface of states, while worsening in others.