Computing the phase diagram of binary mixtures: A patchy particle case study (original) (raw)
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Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches
2010
We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, AAA. The only difference between species is the number of their patches -or functionality-, fA(1)f_A^{(1)}fA(1) and fA(2)f_A^{(2)}fA(2) (with fA(2)>fA(1)f_A^{(2)}>f_A^{(1)}fA(2)>fA(1)). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percolated) fluid regime. In particular, when fA(2)ge2fA(1)f_A^{(2)}\ge2f_A^{(1)}fA(2)ge2fA(1) the entropy of bonding drives the phase separation of two network fluids which is absent in other mixtures. This changes drastically the critical properties of the system and drives a change in the topology of the phase diagram (from type I to type V) when fA(1)>2f_A^{(1)}>2fA(1)>2. The difference in functionality also determines the miscibility at high (osmotic) pressures. If fA(2)−fA(1)=1f_A^{(2)}-f_A^{(1)}=1fA(2)−fA(1)=1 the mixture is completely miscible at high pressures, while closed miscibility gaps at pressures above the highest critical pressure of the pure fluids are present if fA(2)−fA(1)>1f_A^{(2)}-f_A^{(1)}>1fA(2)−fA(1)>1. We argue that this phase behaviour is driven by a competition between the entropy of mixing and the entropy of bonding, as the latter dominates in the network fluid regime.
The phase behavior of two-dimensional symmetrical mixtures
The Journal of Chemical Physics, 2010
Using Monte Carlo simulation methods in the grand canonical and semigrand canonical ensembles, we study the phase behavior of two-dimensional symmetrical binary mixtures of Lennard-Jones particles subjected to a weakly corrugated external field of a square symmetry. It is shown that the both vapor-liquid condensation and demixing transition in the liquid phase are not appreciably affected by a weakly corrugated external field. On the other hand, even a weakly corrugated external field considerably influences the structure of solid phases and the liquid-solid transition. In particular, the solid phases are found to exhibit uniaxially ordered distorted hexagonal structure. The triple point temperature increases with the corrugation of the external field, while the triple point density becomes lower when the surface corrugation increases. The changes in the location of the triple point are shown to lead to the changes of the phase diagram topology. It is also demonstrated that the solid phase undergoes a demixing transition, which is also very slightly affected by the weakly corrugated external potential. The demixing transition in the solid phase is shown to belong to the universality class of the Ising model.
Phase diagram of highly asymmetric binary hard-sphere mixtures
Physical Review E, 1999
We study the phase behavior and structure of highly asymmetric binary hard-sphere mixtures. By first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise ͑depletion͒ potential approximation to this effective Hamiltonian in computer simulations, we determine fluid-solid coexistence for size ratios qϭ0.033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for qр0.05 and a fluid-fluid transition for qр0.10. However, the latter remains metastable with respect to the fluid-solid transition for all size ratios we investigate. In the limit q→0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for qу0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit qϭ1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures. ͓S1063-651X͑99͒07805-8͔
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:
Physical Review Letters, 1999
We study the phase behavior of additive binary hard-sphere mixtures by direct computer simulation, using a new technique which exploits an analog of the Gibbs adsorption equation. The resulting phase diagrams, for size ratios q 0.2, 0.1, and 0.05, are in remarkably good agreement with those obtained from an effective one-component Hamiltonian based on pairwise additive depletion potentials, even in regimes of high packing (solid phases) and for relatively large size ratios (q 0.2) where one might expect the approximation of pairwise additivity to fail. Our results show that the depletion potential description accounts for the key features of the phase equilibria for q # 0.2.
Predicting the phase behavior of mixtures of active spherical particles
arXiv (Cornell University), 2016
An important question in the field of active matter is whether or not it is possible to predict the phase behaviour of these systems. Here, we study the phase coexistence of binary mixtures of torque-free active Brownian particles, for both systems with purely repulsive interactions and systems with attractions. Using Brownian dynamics simulations, we show that phase coexistences can be predicted quantitatively for these systems by measuring the pressure and "reservoir densities". Specifically, in agreement with previous literature, we find that the coexisting phases are in mechanical equilibrium, i.e. the two phases have the same pressure. Importantly, we also demonstrate that the coexisting phases are in chemical equilibrium by bringing each phase into contact with particle reservoirs, and showing that for each species these reservoirs are characterized by the same density for both phases. Using this requirement of mechanical and chemical equilibrium we accurately construct the phase boundaries from properties which can be measured purely from the individual coexisting phases. This result highlights that torque-free active Brownian systems follow simple coexistence rules, thus shedding new light on their thermodynamics.
2010
Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes for simulating models of such systems are hamstrung by the difficulty of relaxing the large species in the presence of the small one. Here we describe how the rejection-free geometrical cluster algorithm (GCA) of Liu and Luijten [Phys. Rev. Lett. 92, 035504 (2004)] can be embedded within a restricted Gibbs ensemble to facilitate efficient and accurate studies of fluid phase behavior of highly sizeasymmetrical mixtures. After providing a detailed description of the algorithm, we summarize the bespoke analysis techniques of Ashton et al. [J. Chem. Phys. 132, 074111 (2010)] that permit accurate estimates of coexisting densities and critical-point parameters. We apply our methods to study the liquid-vapor phase diagram of a particular mixture of Lennard-Jones particles having a 10:1 size ratio. As the reservoir volume fraction of small particles is increased in the range 0-5%, the critical temperature decreases by approximately 50%, while the critical density drops by some 30%. These trends imply that in our system, adding small particles decreases the net attraction between large particles, a situation that contrasts with hard-sphere mixtures where an attractive depletion force occurs. arXiv:1007.3686v1 [cond-mat.soft]
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.
Phase diagram and structural properties of a simple model for one-patch particles
Journal of Chemical …, 2009
We study the thermodynamic and structural properties of a simple, one-patch fluid model using the reference hypernetted-chain (RHNC) integral equation and specialized Monte Carlo simulations. In this model, the interacting particles are hard spheres, each of which carries a single identical, arbitrarily-oriented, attractive circular patch on its surface; two spheres attract via a simple squarewell potential only if the two patches on the spheres face each other within a specific angular range dictated by the size of the patch. For a ratio of attractive to repulsive surface of 0.8, we construct the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs ensemble and grand canonical Monte Carlo simulations. We find that RHNC provides a quick and highly reliable estimate for the position of the fluid-fluid critical line. In addition, it gives a detailed (though approximate) description of all structural properties and their dependence on patch size.