The condensation and ordering of models of empty liquids

Abstract

Abstract:We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional offlattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales -and the corresponding empty fluid regime -is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C)

Three-dimensional patchy lattice model for empty fluids

“…Simulations of larger and larger systems are thus required to obtain reliable results, rendering the computation of phase equilibria in the neighborhood of r = 1 3 prohibitive. 14 In this paper we present results that clarify the role of the 1 3 threshold and the universality of the empty fluid regime reported earlier. We consider a model consisting of particles with twelve bonding sites ("patches"), two of type A and ten of type B, on the face centered cubic lattice, and investigate its global phase behavior by simulation and theory.…”

“…The 2A10B model with BB = 0 and r = AB / ≤ 1 2 may exhibit two phase transitions (as in 2D 14 ) which are interpreted as a liquid-vapor transition, and an order disorder transition, the latter occurring at a higher density when both transitions occur at a given temperature.…”

“…13 In a previous paper we considered the 2A2B model consisting of particles with four patches, two of type A and two of type B, on the square lattice and investigated its global phase behavior by simulations and theory. 14 We have set the BB interaction to zero and calculated the phase diagram, as a function of r. We found that, in the same range of parameters as in the 3D off-lattice models, the liquid-vapor diagram exhibits a reentrant shape, 14 with a region where the system exhibits empty fluid behavior. 15 In addition, below r = 1 3 condensation ceases to exist, while the reentrant regime disappears for r > 1 2 , in line with the results for 3D off-lattice models and the predictions of Wertheim's theory.…”

“…[4][5][6][7] When r < 1 3 the gain in entropy resulting from the AB bonds does not balance the loss in energy of the favored AA bonds, in line with the simulation results. 6,7,14 This led us to suggest that the thresholds predicted by Wertheim's theory are exact and universal, i.e., independent of the dimensionality of the system and of the lattice structure.…”

“…The model is a 3D counterpart of the 2A2B model on the square lattice. 14 We develop efficient sampling algorithms to simulate the empty liquid at low temperatures and observed liquid-vapor coexistence in systems with r < 1 3 . We establish a new non-universal threshold r m < 1 3 for liquid-vapor equilibrium (LVE) and Wertheim's first-order perturbation theory suggests the existence of a new regime where the reentrant behavior is so extreme that the low temperature binodal closes at a lower critical point.…”