Stability of phases of a square-well fluid within superposition approximation

Abstract

The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a "near-critical region" where monotonically decaying correlations acquire very long range, although the system never loses stability.

Communication: Nonexistence of a critical point within the Kirkwood superposition approximation

“…[7][8][9] However, our purely analytic result is much more general. It shows in particular that the predictions of the mean-field criticality in the dimensions d > 4 obtained in Ref.…”

“…1-3 However, combined analytic and numerical attempts to derive from the integral equation the existence of a liquid-vapor critical point in three dimensions failed. [4][5][6][7][8][9] Only a "near-critical" behavior could be revealed, with the correlation functions attaining very long, but finite range. Interestingly, it was hypothesized that the critical behavior under KSA approximation depends on the dimensionality of the system, 7,8 with the true criticality present only for d ≥ 5.…”

A Euclidean perspective on the unfolding of azurin: chain motion

“…In addition, the liquid-gas transition and critical phenomena are driven by long-range attractive interactions. This characterization of the factors influencing the stability of phases was shown to follow from a rigorous analysis of equations derived from the distribution function theory of liquids for a system of rigid spheres of diameter σ surrounded by an attractive core of strength ε, which extends to separations Rσ [22]. …”

Multi-particle critical correlations

“…This leaves a question on whether the KSA would lead to the same conclusion when applied as a closure to the Yvon-Born-Green hierarchy [3,5]. However, numerical results combined with analytical techniques [22][23][24][25][26][27] suggest that also in this case a true critical behaviour does not appear for three-dimensional systems. A challenging theoretical problem is to work out an exact analytic answer also to this question.…”