The phase behavior of two-dimensional symmetrical mixtures (original) (raw)
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Two-Dimensional Symmetrical Mixtures in an External Field of Square Symmetry
The Journal of Physical Chemistry B, 2010
Using the Monte Carlo simulation method in the grand canonical ensemble, we study two-dimensional symmetrical binary mixtures subjected to an external potential of square symmetry and finite corrugation. The results reveal a rich variety of mixed liquid-like and solid-like structures. It is demonstrated that even very weakly corrugated external potential leads to the development of axially ordered striped solid-like phases. The results of finite temperature simulation confirm quite well the predictions stemming from the ground state considerations and show the formation of commensurate, high-order commensurate, and incommensurate mixed phases. It is also shown that the corrugation potential affects the demixing transition.
Phase behavior of a symmetrical binary fluid mixture
We have investigated the phase behaviour of a symmetrical binary fluid mixture for the situation where the chemical potentials µ1 and µ2 of the two species differ. Attention is focused on the set of interparticle interaction strengths for which, when µ1 = µ2, the phase diagram exhibits both a liquidvapor critical point and a tricritical point. The corresponding phase behaviour for the case µ1 = µ2 is investigated via integral-equation theory calculations within the mean spherical approximation (MSA), and grand canonical Monte Carlo (GCMC) simulations. We find that two possible subtypes of phase behaviour can occur, these being distinguished by the relationship between the critical lines in the full phase diagram in the space of temperature, density, and concentration. We present the detailed form of the phase diagram for both subtypes and compare with the results from GCMC simulations, finding good overall agreement. The scenario via which one subtype evolves into the other, is also studied, revealing interesting features.
Phase behaviour of very asymmetric binary mixtures
Journal of Physics: Condensed Matter, 2000
The phase behaviour of very asymmetric binary mixtures can be understood in terms of the depletion interaction. For hard particles this yields a narrow deep attractive well surrounding the hard core. Colloids with similar interaction potentials are known to destabilize the liquid, causing it to show a wide fluid-solid coexistence, and in extreme cases they exhibit an exotic solid-solid condensation. For a mixture this means that phase separation is not fluid-fluid, as previously thought, but normally fluid-solid, and if the asymmetry is very large, even solid-solid. We present in this work the result of devising a density functional theory for an infinitely asymmetric mixture of parallel hard cubes. This model is singular and undergoes a collapse in a close-packed solid (an extreme fluid-solid demixing). We avoid this collapse by introducing a small amount of polydispersity in the large particles; the resulting phase diagram shows the fluid-solid and solid-solid demixing scenarios described above. † Current address:
Journal of Molecular Liquids, 2011
The generalised Frenkel-Louis model, which is defined for asymmetric binary mixture of large hexagonal and small rhombus particles on a hexagonal lattice, is exactly solved by establishing a rigorous mapping equivalence with the one-component lattice-gas model and the corresponding spin-1/2 Ising model on a triangular lattice. This precise approach enables one to investigate in detail how the phase separation and critical behaviour in a close vicinity of demixing depends on pressure and inter-particle interactions. The binary mixture with the attractive inter-particle interaction exhibits diverse coexistence curves including asymmetric liquid-vapour coexistence curves, symmetric or asymmetric liquid-liquid coexistence curves, while asymmetric liquid-liquid coexistence curves always occur in the binary system with the repulsive inter-particle interaction.
Grand canonical simulation of phase behaviour in highly size-asymmetrical binary fluids
Molecular Physics, 2011
We describe a Monte Carlo scheme for the grand canonical simulation study of fluid phase equilibria in highly size-asymmetrical binary mixtures. The method utilizes an expanded ensemble in which the insertion and deletion of large particles is accomplished gradually by traversing a series of states in which a large particle interacts only partially with the environment of small particles. Free energy barriers arising from interfacial coexistence states are surmounted with the aid of multicanonical preweighting, the associated weights being determined from the transition matrix. As an illustration, we present results for the liquid-vapour coexistence properties of a Lennard-Jones binary mixture having a 10 : 1 size ratio. arXiv:1002.2844v1 [cond-mat.soft]
The condensation and ordering of models of empty liquids
arXiv preprint arXiv: …, 2011
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, * AB , varies. In line with previous work, on threedimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of * 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.
Physica A: Statistical Mechanics and its Applications, 1999
We performed Monte Carlo simulation of the phase diagram of a two-dimensional lattice with the nearest-neighbor attraction on a hexagonal lattice. A fraction of sites is rigidly ÿxed in a disordered conÿguration in order to mimic quenched absorbent (matrix). It is shown that the phase diagram of this partly quenched system is essentially narrower and the critical temperature is lower, compared with the bulk system, i.e. without matrix. Moreover, a liquid-like branch of the coexistence envelope has a speciÿc shape. It is shown that di erent, thermodynamically equivalent, matrix conÿgurations result in a slightly di erent gas-liquid critical temperature. We have analyzed profoundly thermodynamic behavior of a uid in each copy of the matrix realization. In particular, the behavior of the heat capacity, of the fourth Binder cumulant, compressibility of a uid along coexistence are analyzed. The pair distribution function of uid species and its blocking term, due to correlations of uid particles via matrix subsystem, have been obtained. The blocking distribution function appears to be more long ranged than the total uid-uid distribution function. The uctuations of the blocking e ects may serve as a measure of the number of matrix realizations necessary to involve in obtaining adequate statistical averages in the partly quenched systems.
Computing the phase diagram of binary mixtures: A patchy particle case study
The Journal of Chemical Physics, 2013
We investigate the phase behaviour of 2D mixtures of bi-functional and three-functional patchy particles and 3D mixtures of bi-functional and tetra-functional patchy particles by means of Monte Carlo simulations and Wertheim theory. We start by computing the critical points of the pure systems and then we investigate how the critical parameters change upon lowering the temperature. We extend the Successive Umbrella Sampling method to mixtures to make it possible to extract information about the phase behaviour of the system at a fixed temperature for the whole range of densities and compositions of interest.
Simulation of Phase Transitions in Highly Asymmetric Fluid Mixtures
Physical Review Letters, 2006
We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs ensemble, we are able to probe directly the density and concentration fluctuations that drive phase transitions, but that are inaccessible to conventional simulation algorithms. We develop a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multicomponent fluids. Several illustrative examples are presented.